We wish to see if the dial indicating the oven temperature for a certain model of oven is properly calibrated. Four ovens of this model are selected at random. The dial on each is set to 300 °F, and, after one hour, the actual temperature of each is measured. The temperatures measured are 305 °F, 310 °F, 300 °F, and 305 °F. Assuming that the actual temperatures for this model when the dial is set for 300° are Normally distributed with mean μ, we test whether the dial is properly calibrated at 5% of significance level.

Actual Temp: 305, 310, 300, 305

Required:
a. Based on the data, calculate the sample standard deviation and standard error of X bar (round them into two decimal places) Standard Deviation: Standard Error:
b. What is a 95% confidence interval for μ? (upper and lower bound)
c. Provide your test statistic and P-value
d. State your conclusion clearly (statistical conclusion and its interpretation).
e. Even if 5% of significance level looks like default of test, we can use different significance levels as well. If we change the significance level into 10% (= 0.1), how does it affect your conclusion?

Answers

Answer 1

Answer:

a. Standard deviation: 4.082

Standard error: 2.041

b. The 95% confidence interval for the actual temperature is (298.5, 311.5).

Upper bound: 311.5

Lower bound: 298.5

c. Test statistic t=2.45

P-value = 0.092

d. There is no enough evidence to claim that the dial of the oven is not properly calibrated. The actual temperature does not significantly differ from 300 °F.

e. If we use a significance level of 10% (a less rigorous test, in which the null hypothesis is rejected with with less requirements), the conclusion changes and now there is enough evidence to claim that the dial is not properly calibrated.

This happens because now the P-value (0.092) is smaller than the significance level (0.10), given statististical evidence for the claim.

Step-by-step explanation:

The mean and standard deviation of the sample are:

[tex]M=\dfrac{1}{4}\sum_{i=1}^{4}(305+310+300+305)\\\\\\ M=\dfrac{1220}{4}=305[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{3}\cdot [(305-(305))^2+(310-(305))^2+(300-(305))^2+(305-(305))^2]}\\\\\\ s=\sqrt{\dfrac{1}{3}\cdot [(0)+(25)+(25)+(0)]}\\\\\\ s=\sqrt{\dfrac{50}{3}}=\sqrt{16.667}\\\\\\s=4.082[/tex]

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=305.

The sample size is N=4.

When σ is not known, s divided by the square root of N is used as an estimate of σM (standard error):

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{4.082}{\sqrt{4}}=\dfrac{4.082}{2}=2.041[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=4-1=3[/tex]

The t-value for a 95% confidence interval and 3 degrees of freedom is t=3.18.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=3.18 \cdot 2.041=6.5[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 305-6.5=298.5\\\\UL=M+t \cdot s_M = 305+6.5=311.5[/tex]

The 95% confidence interval for the actual temperature is (298.5, 311.5).

This is a hypothesis test for the population mean.

The claim is that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=300\\\\H_a:\mu\neq 300[/tex]

The significance level is 0.05.

The sample has a size n=4.

The sample mean is M=305.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.028.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.082}{\sqrt{4}}=2.041[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{305-300}{2.041}=\dfrac{5}{2.041}=2.45[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=4-1=3[/tex]

This test is a two-tailed test, with 3 degrees of freedom and t=2.45, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>2.45)=0.092[/tex]

As the P-value (0.092) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.

If the significance level is 10%, the P-value (0.092) is smaller than the significance level (0.1) and the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °C does not significantly differ from 300 °C.


Related Questions

In a class of 30 students, there are four more girls than boys. a)Using x as the number of boys, write down an equation b)Solve the equation and find the number of girls in the class.

Answers

easy claps!!

Answer: 30=2x+4 and there are 17 girls in the class.

Step-by-step explanation: if x+4=[total girls] and x=[total boys] and 30=[total kids], then x+4+x = 2x+4 = [total kids], since total kids id 30 then our equation is 30 = 2x + 4 and x= 13boys so 30-13= 17girls.

It's BASIC prealgebra so you should probably practice bit more with linear equations!

what is the output from the following machine when the input is 4

Answers

Answer:

4 - 7 = -3

-3 / 3 = -1

What they said is correct

The following data summarizes results from 1000 ​pre-employment drug screening tests. If one of the test subjects is randomly​ selected, find the probability that the subject had a positive test result or a negative test result.
Positive Test Result Negative Test Result
Subject Uses Drugs 76 6
Subject Is Not a Drug User 95 823
P (subject had a positive test result or a negative test result)= simplify your answer.

Answers

Answer:

P (subject had a positive test result or a negative test result) = 1

Step-by-step explanation:

Given

The table above

Required

P (subject had a positive test result or a negative test result)

This is calculated as follows;

P (subject had a positive test result or a negative test result) =

P (subject had a positive test result) + P (subject had a negative test result)

Calculating P (subject had a positive test result)

This can be calculated by number of subjects with positive results divided by 1000

Only data from the column of subjects with positive results will be considered.

Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs

Number of subjects = 76 + 95

Number of Subjects = 171

P (Subject had a positive test Result) = 171/1000

Calculating P (subject had a negative test result)

This can be calculated by number of subjects with negative results divided by 1000

Only data from the column of subjects with negative results will be considered.

Number of Subjects = Subjects that uses drugs + Subjects that do not use drugs

Number of subjects = 6 + 823

Number of Subjects = 829

P (Subject had a negative test Result) = 829/1000

Hence, P (subject had a positive test result or a negative test result) =

P (subject had a positive test result) + P (subject had a negative test result) = 171/1000 + 829/1000

P (subject had a positive test result or a negative test result) = (171 + 829)/1000

P (subject had a positive test result or a negative test result) = 1000/1000

P (subject had a positive test result or a negative test result) = 1

Evaluate each expression. 16 5/4 x 16 1/4 / (16 1/2)/2= ​

Answers

Answer: the answer is 4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4 on edgunity 2020

A sports physician conducts an observational study to learn the average amount of time that 3,000 swimmers in the town can hold their breath underwater. He uses 150 sampling of 60 people. The average of the means of all the samplings is 72.7, and the standard deviation is 0.92. This is a histogram of the sampling distribution of the sample mean

Answers

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

A sports physician conducts an observational study to learn the average amount of time that 3,000 swimmers in the town can hold their breath underwater. He uses 150 sampling of 60 people. The average of the means of all the samplings is 72.7, and the standard deviation is 0.92. This is a histogram of the sampling distribution of the sample mean. Based on this data, with a 95% confidence interval the researchers can determine that the actual average amount of time the entire population can hold their breath under water is?

Given Information:

sample mean time = 72.7

sample standard deviation = 0.92

Sampling size = n = 150

Confidence level = 95%

Required Information:

95% confidence interval = ?  

Answer:

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]

Step-by-step explanation:

The confidence interval is given by

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean time and Margin of error is given by

[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]

Where n is the sampling size, s is the sample standard deviation, and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to 95% confidence level.

The t-score corresponding to 95% confidence level is

Significance level = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 150 - 1 = 149

From the t-table at α = 0.025 and DoF = 149

t-score = 1.975

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 1.975\cdot \frac{0.92}{\sqrt{150} } \\\\MoE = 1.96\cdot 0.07512\\\\MoE = 0.14836\\\\[/tex]

So the required 95% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 72.7 \pm 0.14836\\\\\text {confidence interval} = 72.7 - 0.14836, \: 72.7 + 0.14836\\\\\text {confidence interval} = (72.552, \: 72.848)\\\\[/tex]

Therefore, we are 95% confident that actual average amount of time the entire population can hold their breath under water is within the range of (72.552, 72.848)

A consultant built an Einstein Analytics dashboard for a shipping company. The dashboard displays data from several data sources. The consultant enabled data sync (replication) to increase the speed of data refreshing from these sources. What is the maximum number of dataflow definitions available in this situation?
A. 30
B. 45
C. 25
D. 35

Answers

Answer: A (30)

Step-by-step explanation:

By defaults, data will be enabled in tens. And it increases by replicating the initial value.

There is no way the maximum number of dataflow definitions available in this situation will be 45, 25 or 35

The only possible replicant that can be available is 30

What’s the correct answer for this?

Answers

Answer:

1) Antonio's statement

2) <A = 123

Step-by-step explanation:

1) Antonio's statement is incorrect. This is because the opposite angles of a quadrilateral add up to 180°. Erin was incorrect because the opposite angles of this quadrilateral are unequal.

2) 2x+7+5x-2 = 180° (opposite angles of quadrilateral)

Now

7x+5 = 180

7x = 175

x = 25

<A = 5x-2

= 5(25)-2

= 125-2

= 123

Can you please help me with this

Answers

Answer:

-The total area of a Rectangular Prism:

[tex]A = 366[/tex] [tex]in^{2}[/tex]

Step-by-step explanation:

-To find the total area of a rectangular prism, you need this formula:

[tex]A = 2(l \cdot w + l \cdot h + w \cdot h)[/tex]

[tex]l =[/tex] Length

[tex]w =[/tex] Width

[tex]h =[/tex] Height

-Apply the length, width and height for the formula:

[tex]A = 2(11 \cdot 8 + 11 \cdot 5 + 8 \cdot 5)[/tex]

[tex]l =[/tex] 11 in

[tex]w =[/tex] 8 in

[tex]h =[/tex] 5 in

-Then, solve for the area:

[tex]A = 2(11 \cdot 8 + 11 \cdot 5 + 8 \cdot 5)[/tex]

[tex]A = 2(88 + 55 + 40)[/tex]

[tex]A = 2(143 + 40)[/tex]

[tex]A = 2 \times 183[/tex]

[tex]A = 366[/tex]

So, the total area would be [tex]366[/tex] [tex]in ^{2}[/tex].

Angelina read 30% of her book containing 360 pages. How many pages has she read so far

Answers

Answer:

108 pages

Step-by-step explanation:

Angelina read 30% of the book that contains 360 pages.

30% of 360 pages

"of" also means multiply, so we must multiply 30% and 360.

30% * 360

Convert 30% to a decimal. Divide 30 by 100, or move the decimal place 2 spots to the left.

30/100=0.30

or

30.0---> 3.0---> 0.30

Plug the decimal in for the percent.

0.30*360

Multiply the 2 numbers together

108

Angelina has read 108 pages so far.

:4. In the Department of Natural Sciences, 14 faculty members have a PhD, and 30 faculty members do not have a PhD. In the Department, the number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD. If a third of the male faculty in the Department have a PhD, then what is the number of female faculty in the Department with a PhD?​

Answers

Answer:

The number of female faculty in the Department with a PhD is 8.

Step-by-step explanation:

There are 14 + 30 = 44 faculty members.

Of those, x are male and y are female.

Then

x + y = 44.

The number of female faculty who do not have a PhD is 10 more than the number of females who have a PhD.

y = z + w

z is the number of females with PhD.

w is the number of females without PhD.

w = z + 10

If a third of the male faculty in the Department have a PhD

[tex]\frac{x}{3} + z = 14[/tex]

Now, we can write all variables as functions of z, which is the number of female faculty in the Department with PhD.

The objective is:

To find z from the first equation, that is:

[tex]x + y = 44[/tex]

To do this, we have to write x and y as functions of z.

Writing x and y as functions z.

[tex]\frac{x}{3} + z = 14[/tex]

[tex]\frac{x}{3} = 14 - x[/tex]

[tex]x = 3(14 - z)[/tex]

[tex]x = 42 - 3z[/tex]

And

[tex]y = z + w[/tex]

In which

[tex]w = 10 + z[/tex]

So

[tex]y = z + 10 + z[/tex]

[tex]y = 2z + 10[/tex]

Replacing:

[tex]x + y = 44[/tex]

[tex]42 - 3z + 2z + 10 = 44[/tex]

[tex]-z + 52 = 44[/tex]

[tex]z = 52 - 44[/tex]

[tex]z = 8[/tex]

The number of female faculty in the Department with a PhD is 8.

Among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol. Suppose five 25- to 30-year-olds are selected at random. Complete parts (a) through (d) below. (a) What is the probability that all five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (b) What is the probability that at least one has not used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (c) What is the probability that none of the five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (d) What is the probability that at least one has used a computer while under the influence of alcohol? (Round to four decimal places as needed.)

Answers

Answer:

(a) The probability that all five have used a computer while under the influence of alcohol is 0.0021.

(b) The probability that at least one has not used a computer while under the influence of alcohol is 0.9979.

(c) The probability that none of the five have used a computer while under the influence of alcohol is 0.1804.

(d) The probability that at least one has used a computer while under the influence of alcohol is 0.8196.

Step-by-step explanation:

We are given that among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol.

Suppose five 25- to 30-year-olds are selected at random.

The above situation can be represented through the binomial distribution;

[tex]P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........[/tex]

where, n = number of trials (samples) taken = Five 25- to 30-year-olds

            r = number of success

            p = probability of success which in our question is probability that

                  people used a computer while under the influence of alcohol,

                   i.e. p = 29%.

Let X = Number of people who used computer while under the influence of alcohol.

So, X ~ Binom(n = 5, p = 0.29)

(a) The probability that all five have used a computer while under the influence of alcohol is given by = P(X = 5)

               P(X = 5)  =  [tex]\binom{5}{5}\times 0.29^{5} \times (1-0.29)^{5-5}[/tex]

                              =  [tex]1 \times 0.29^{5} \times 0.71^{0}[/tex]

                              =  0.0021

(b) The probability that at least one has not used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)

Here, the probability of success (p) will change because now the success for us is that people have not used a computer while under the influence of alcohol = 1 - 0.29 = 0.71

SO, now X ~ Binom(n = 5, p = 0.71)

               P(X [tex]\geq[/tex] 1)  =  1 - P(X = 0)   

                              =  [tex]1-\binom{5}{0}\times 0.71^{0} \times (1-0.71)^{5-0}[/tex]

                              =  [tex]1 -(1 \times 1 \times 0.29^{5})[/tex]

                              =  1 - 0.0021 = 0.9979.

(c) The probability that none of the five have used a computer while under the influence of alcohol is given by = P(X = 0)

               P(X = 0)  =  [tex]\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]

                              =  [tex]1 \times 1 \times 0.71^{5}[/tex]

                              =  0.1804

(d) The probability that at least one has used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)

               P(X [tex]\geq[/tex] 1)  =  1 - P(X = 0)   

                              =  [tex]1-\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]

                              =  [tex]1 -(1 \times 1 \times 0.71^{5})[/tex]

                              =  1 - 0.1804 = 0.8196

Please answer this correctly

Answers

Answer:

2

Step-by-step explanation:

Set the height of the bar to 2 since there are 2 numbers between 21-40.

Answer:

2 people.

Step-by-step explanation:

34 minutes and 40 minutes were recorded.

Therefore, 2 people.

On Sunday, a local hamburger shop sold a combined of 572 hamburger and cheeseburger. The number of cheeseburgers sold was three times the number of hamburger sold. How many hamburger were sold on Sunday

Answers

Answer: 143 hamburgers and 429 cheese burgers

Explanation:

Call h and c the number of both items.
(h-hamburger and c-cheeseburger)

h + c = 572
c = 3h

Sub the second into the first

h + 3h = 572
4h = 572

Divide both sides by 4
h = 143 hamburgers

Use this back into the second equation
c = 3 • 143 = 429 cheeseburgers

A study was conducted to determine if the salaries of librarians from two neighboring cities were equal. A sample of 15 librarians from each city was randomly selected. The mean from the first city was $28,900 with a standard deviation of $2300. The mean from the second city was $30,300 with a standard deviation of $2100. Construct a 95% confidence interval for u1 -u2.
a) (-4081, 597)
b) (-2054, 238)
c) (-2871, 567)
d) (-3125, 325)

Answers

Answer:

Step-by-step explanation:

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

Where

x1 = sample mean salary of city 1 librarians

x2 = sample mean salary of city 2 librarians

s1 = sample standard deviation for city 1

s2 = sample standard deviation for city 2

n1 = number of soles for city 1

n1 = number of soles for city 2

For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small

Degree of freedom =

(n1 - 1) + (n2 - 1) = (15 - 1) + (15 - 1) = 28

z = 2.048

x1 - x2 = 28,900 - 30,300 = - 1400

Margin of error = 2.048√(s1²/n1 + s2²/n2) = 2.036√(2300²/15 + 2100²/15)

= 1647

The upper boundary for the confidence interval is

- 1400 + 1647 = 247

The lower boundary for the confidence interval is

- 1400 - 1647 = - 3047

Find the area of a circle with radius, r = 6.89m.

Give your answer rounded to 2 DP (2 decimal points)


The photo is attached below

Answers

Answer:

149.14 [tex]m^{2}[/tex]

Step-by-step explanation:

Area of a circle = π[tex]r^{2}[/tex]

so A = π * 6.89^2 = 149.14 (to 2d.p.)

In ΔEFG, ∠E \cong≅∠G, GE = 7 and FG = 15. Find the length of EF.

Answers

Answer:  EF = 15

Step-by-step explanation:

The given description is that of an isosceles triangle. The base angles are congruent, therefore the sides opposite of those angles are also congruent.

The base angles are ∠E and ∠G and the vertex angle is ∠F.

The sides opposite to the base angles are EF and FG.

Thus, EF ≡ FG.

Since FG = 15 and FG = EF, then 15 = EF.

Based on the definition of an isosceles triangle, the length of EF in the triangle is: 15 units.

What is an Isosceles Triangle?

An isosceles triangle has two sides that are congruent. The angles opposite these congruent sides are also congruent.

ΔEFG is an isosceles triangle. The congruent sides are, FG and EF.

Therefore, EF = FG = 15 units.

Learn more about isosceles triangle on:

https://brainly.com/question/11884412

A bank is investigating ways to entice customers to charge more on their credit cards. (Banks earn a fee from the merchant on each purchase, and hope to collect interest from the customers, as well.) A bank selects a random group of customers who are told their "cash back" will increase from 1% to 2% for all charges above a certain dollar amount each month. Of the 500 customers who were told the increase applied to charges above $1000 each month, the average increase in spending was $527 with a standard deviation of $225. Of the 500 customers who were told the increase applied to charges above $2000 each month, the average increase in spending was $439 with a standard deviation of $189. A level C = 95% confidence interval for \mu_1\:-\:\mu_2μ 1 − μ 2 is approximated by Group of answer choices (62.2, 113.8) (86.2, 120.5) (10.3, 23.8) (55.6, 67.8)

Answers

Answer:

[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]

[tex]CI = (527 - 439) \pm 25.75\\\\CI = 88 \pm 25.75\\\\CI = 88 - 25.75 \:\: and \:\: 88 + 25.75\\\\CI = (62.2 \: ,\: 113.8 )[/tex]

The correct answer choice is a. (62.2, 113.8)

Step-by-step explanation:

Of the 500 customers who were told the increase applied to charges above $1000 each month, the average increase in spending was $527 with a standard deviation of $225.

Sample size = n₁ = 500

Sample mean = x₁ = $527

Standard deviation = s₁ = $225

Of the 500 customers who were told the increase applied to charges above $2000 each month, the average increase in spending was $439 with a standard deviation of $189

Sample size = n₂ = 500

Sample mean = x₂ = $439

Standard deviation = s₂ = $189

We are asked to find the 95% confidence interval for the difference between two means.

The given group of answer choices are

a. (62.2, 113.8)

b. (86.2, 120.5)

c. (10.3, 23.8)

d. (55.6, 67.8)

The confidence interval for the difference between two means is given by

[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]

Where [tex]\bar{x_{1} }[/tex] and [tex]\bar{x_{2} }[/tex] are the given sample means and margin of error is given by

[tex]$ MoE = z_{\alpha/2} \cdot \sqrt{\frac{s_{1}^2}{n_1} + \frac{s_{2}^2}{n_2}} $[/tex]

The z-score corresponding to 95% confidence level is given by

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

From the z-table at α = 0.025 the z-score is 1.96

[tex]$ MoE = 1.96 \cdot \sqrt{\frac{225^2}{500} + \frac{189^2}{500}} $[/tex]

[tex]MoE = 1.96 \cdot 13.14[/tex]

[tex]MoE = 25.75[/tex]

Finally,

[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]

[tex]CI = (527 - 439) \pm 25.75\\\\CI = 88 \pm 25.75\\\\CI = 88 - 25.75 \:\: and \:\: 88 + 25.75\\\\CI = (62.2 \: ,\: 113.8 )[/tex]

Therefore, the correct answer choice is a. (62.2, 113.8)

How to use z-table?

In the z-table find the probability of 0.025

Note down the value of that row, it would be 1.9.

Note down the value of that column, it would be 0.06.

Add the two numbers together.

The z-score is 1.9 + 0.06 = 1.96

The market and Stock J have the following probability distributions:
Probability rM rJ
0.3 14% 22%
0.4 10 4
0.3 19 12
1. Calculate the expected rate of return for the market. Round your answer to two decimal places.%
2. Calculate the expected rate of return for Stock J. Round your answer to two decimal places.%
3. Calculate the standard deviation for the market. Round your answer to two decimal places.%
4. Calculate the standard deviation for Stock J. Round your answer to two decimal places.%

Answers

Answer:

1) [tex] E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%[/tex]

2) [tex]E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%[/tex]

3) [tex] E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1 [/tex]

And the variance would be given by:

[tex]Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{13.89}= 3.73[/tex]

4) [tex] E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8 [/tex]

And the variance would be given by:

[tex]Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{55.56}= 7.45[/tex]

Step-by-step explanation:

For this case we have the following distributions given:

Probability  M   J

0.3           14%  22%

0.4           10%    4%

0.3           19%    12%

Part 1

The expected value is given by this formula:

[tex] E(X)=\sum_{i=1}^n X_i P(X_i)[/tex]

And replacing we got:

[tex] E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%[/tex]

Part 2

[tex]E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%[/tex]

Part 3

We can calculate the second moment first with the following formula:

[tex] E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1 [/tex]

And the variance would be given by:

[tex]Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{13.89}= 3.73[/tex]

Part 4

We can calculate the second moment first with the following formula:

[tex] E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8 [/tex]

And the variance would be given by:

[tex]Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56[/tex]

And the deviation would be:

[tex] Sd(M) = \sqrt{55.56}= 7.45[/tex]

what is the solution set for the equation (x+3)(x-8)=0

Answers

Answer:

x = -3        x=8

Step-by-step explanation:

(x+3)(x-8)=0

Using the zero product property

x+3 =0   x -8 = 0

x = -3        x=8

A start-up news company is looking to expand their audience and is interested in studying the how many adults regularly use social media as a source of news. According to the Pew Research Center, 62% of adults get their news from social media, but researchers want to determine of this proportion is actually greater than 62% in region they plan on advertising on.
They take a random sample of 200 adults in the region they are interested in advertising in and what they use to typically get their news. A total of 137 adults reported regularly getting their news from social media.
The point estimate for this problem is: (report your answer to 3 decimal places)
Checking Conditions: We are told that the sample was randomly selected. Are the other conditions met to perform a hypothesis test for p?
A) Yes, the sample size is greater than 30.
B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.
C) Yes, the population standard deviation is known.
D) No, the population mean is unknown.

Answers

Answer:

Step-by-step explanation:

The point estimate is the sample proportion.

Considering the sample,

Sample proportion, p = x/n

Where

x = number of success = 137

n = number of samples = 200

p = 137/200 = 0.685

From the information given,

Population proportion = 62% = 62/100 = 0.62

The correct options are

A) Yes, the sample size is greater than 30.

B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.

What’s the correct answer for this?

Answers

Answer:

(2,-2)

Step-by-step explanation:

In the attached file

Triangle XYZ is translated so that X’ is that (4,-2) which rule defines this translation?

Answers

Answer: y

Step-by-step explanation:

According to a polling​ organization, 22​% of adults in a large region consider themselves to be liberal. A survey asked 200 respondents to disclose their political​ philosophy: Conservative,​ Liberal, Moderate. Treat the results of the survey as a random sample of adults in this region. Do the survey results suggest the proportion is higher than that reported by the polling​ organization? Use an alphaequals0.01 level of significance.

Answers

Answer:

No. There is not enough evidence to support the claim that the proportion of liberals is higher than that reported by the polling​ organization (P-value = 0.0366).

Step-by-step explanation:

The question is incomplete: there is no information about the results of the survey. We will assume that 55 of the subjects answer "liberal", and test the claim.

This is a hypothesis test for a proportion.

The claim is that the proportion of liberals is higher than that reported by the polling​ organization.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.22\\\\H_a:\pi>0.22[/tex]

The significance level is 0.01.

The sample has a size n=200.

The sample proportion is p=0.275.

[tex]p=X/n=55/200=0.275[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.22*0.78}{200}}\\\\\\ \sigma_p=\sqrt{0.000858}=0.029[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.275-0.22-0.5/200}{0.029}=\dfrac{0.053}{0.029}=1.792[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>1.792)=0.0366[/tex]

As the P-value (0.0366) is greater than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the proportion of liberals is higher than that reported by the polling​ organization.

A street performer earns 40% of all his daily earnings at the barclays center subway station.He earns about $60 at that station. Assuming he works everyday and earns the same amount, how much does he earn in two weeks?

Answers

Answer:

He earns $2,100 in two weeks.

Step-by-step explanation:

We know that this street performers earn $60 per day at the Barclays center subway station, and that this earning represents 40% (or a proportion of 0.4) of his daily earnings. We can calculate his daily earnings as:

[tex]0.4D=\$\,60\\\\D=\dfrac{\$\,60}{0.4}=\$\,150[/tex]

If the daily earnings are $150, the earnings in 2 weeks (14 days) will be:

[tex]W=14\cdot\$\,150=\$\,2100[/tex]

if r is the radius of a circle and d is its diameter which of the following is an equivalent formula for the circumference c = 2 pie r
a C = pie d2
b C = pie rd
c C = pie d
d C = 2 pie d

Answers

Answer:

C

Step-by-step explanation:

C=2pier or pied

Answer:

a. C = 2πr

c. C= πd

both are correct

Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in​ "hic," which is a measurement of a standard​ "head injury​ criterion," (lower ​ "hic" values correspond to safer​ cars). The listed values correspond to cars​ A, B,​ C, D,​ E, F, and​ G, respectively. Find the
a.​ mean,
b.​ median,
c.​ midrange,
d. mode for the data.
Also complete parts e. and f. 514 541 302 400 507 406 369

Answers

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in​ "hic," which is a measurement of a standard​ "head injury​ criterion," (lower ​ "hic" values correspond to safer​ cars). The listed values correspond to cars​ A, B,​ C, D,​ E, F, and​ G, respectively.

514 541 302 400 507 406 369

Find the

a.​ mean,

b.​ median,

c.​ midrange,

d. mode for the data.

Also complete parts e. and f.

e. Which car appears to be the safest?

f. Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?

Answer:

a) Mean = 434.14

b) Median = 406

c) Midrange = 421.5

d) Mode = 0

e) Car C appears to be the safest

f) The small cars does not appear to have about the same risk of head injury in a crash.

Step-by-step explanation:

We are given the head injury measurements from small cars that were tested in crashes.

The measurements are in​ "hic," which is a measurement of a standard​ "head injury​ criterion.

The listed values are;

A = 514

B = 541

​C = 302

D = 400

​E = 507

F = 406

G = 369

a)​ Mean

The mean of the measurements is given by

Mean = Sum of measurements/ Number of measurements

Mean = (514 + 541 + 302 + 400 + 507 + 406 + 369)/7

Mean = 3039/7

Mean = 434.14

b)​ Median

Arrange the measurements in ascending order (low to high)

302, 369, 400, 406, 507, 514, 541

The median is given by

Median = (n + 1)/2

Median = (7 + 1)/2

Median = 8/2

Median = 4th

Therefore, the 4th measurement is the median that is 406

Median = 406

c)​ Mid-range

The midrange is given by

Midrange = (Max + Min)/2

The maximum measurement in the data set is 541

The minimum measurement in the data set is 302

Midrange = (541 + 302)/2

Midrange = 843/2

Midrange = 421.5

d)​ Mode for the data

The mode of the data set is the most repeated measurement.

302, 369, 400, 406, 507, 514, 541

In the given data set we don't have any repeated measurement therefore, there is no mode or we can say the mode of this data set is 0.

Mode = 0

e) Which car appears to be the safest?

Since we are given that the measurements are in​ "hic," which is a measurement of a standard​ "head injury​ criterion," (lower ​ "hic" values correspond to safer​ cars)

The lowest hic value corresponds to car C that is 302

Therefore, car C appears to be the safest among other cars.

f) Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?

302, 369, 400, 406, 507, 514, 541

As you can notice, the hic values differ a lot from each other therefore, we can conclude that the small cars does not appear to have about the same risk of head injury in a crash.

Please answer this correctly

Answers

Answer:

Look at the money bags below!!! (but I'll give you the answer)

Step-by-step explanation:

John F: 7 full bags - 1 half

Juan A: 9 full bags

Jason A: 3 full bags

Nick J: 3 full bags- 1 half

Alfonso S: 8 full bags

Hope this helped and wasn't confusing!!! xx - Asia

A rectangular fish tank is 50 cm​ long, 40 cm​ wide, and 20 cm high. ​a) How many cubic centimeters of water will the tank​ hold? ​b) How many milliliters of water will the tank​ hold? ​c) How many liters of water will the tank​ hold?

Answers

Answer:

40 litres

Step-by-step explanation:

V = l x w x h

50 x 40 x 20 = 40000

40000 cm^3

1cm^3 = 1ml

40000 cm^3/ 1cm^3 = 40000ml

40000 x 10^-3 = 40 litres

If the figures below are similar, find the scale factor of Figure B to Figure A.
48
27
60
А
16
B
20
9

Answers

Answer:

The scale factor is 3.

Step-by-step explanation

Figure B has side measures 16, 20, and 9. Figure A has side measures 48, 27, and 60. The ratio of each of the corresponding sides is 1:3 (16:48, etc). Therefore, the scale factor of Figure B to Figure A is 3.

45 units and is centered at


A circle has a radius of


(-2.4, -4.8).


What is the equation of this circle?

Answers

The correct question is:

A circle has a radius of 45 units and is centered at (-2.4, -4.8).

What is the equation of this circle?

Answer:

Equation of the circle is;

(x + 2.4)² + (y + 4.8)² = 2304

Step-by-step explanation:

The standard equation of a circle is;

(x - a)² + (y - b)²  =  r²

where;

(a,b) is the center of the circle and r is the radius of the circle

Now, from the question, the circle is centered at (-2.4, -4.8) and the radius is 45

Thus, plugging those values into the standard form of equation of a circle, we have;

(x - (-2.4))²  +  (y - (-4.8))²  = 48²

This gives;

(x + 2.4)² + (y + 4.8)² = 2304

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