It is believed that approximately 12% of the population of the United States is lefthanded. Suppose researchers suspect that the proportion of left-handed people is higher in certain states than the national average. The researchers conduct a sample of 200 randomly selected people in the state of Maine and find that 29 people in the sample are left-handed.
a. Write the null hypothesis and alternative hypothesis and define your parameter.
b. Show that the necessary conditions (Randomization Condition, 10% Condition, Sample Size Condition) are satisfied to perform a hypothesis test. Briefly explain how each condition is satisfied.
c. Perform the hypothesis test and find the P-value. (To show your work: Write down what values you are entering into the hypothesis testing calculator.)
d. Is there strong evidence that the left-handed rate in the state of Maine is higher than the national average? Briefly explain how you know.

Multiply 2 by 1/2 to get 1.

Multiply 1 by 2/3 to get 2/3.

Multiply 2/3 by 3/4 to get 6/12 = 1/2.

Multiply 1/2 by 4/5 to get 4/10 = 2/5.

Multiply 2/5 by 5/6 to get 10/30 = 1/3.

Multiply 1/3 by 6/7 to get 6/21 = 2/7. (I suspect there's a typo in the question.)

And so on, so that the nth term in the sequence is multiplied by n/(n + 1) to get the (n + 1)th term.

Recursively, the sequence is given by

[tex]\begin{cases}a_1=2\\a_n=\dfrac{n-1}na_{n-1}&\text{for }n>1\end{cases}[/tex]

We can solve this exactly by iterating:

[tex]a_n=\dfrac{n-1}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}{n-1}\dfrac{n-3}{n-2}a_{n-3}=\cdots[/tex]

and so on down to

[tex]a_n=\dfrac{(n-1)\cdot(n-2)\cdot(n-3)\cdot\cdots\cdot3\cdot2\cdot1}{n\cdot(n-1)\cdot(n-2)\cdot\cdots\cdot4\cdot3\cdot2}a_1[/tex]

or

[tex]a_n=\dfrac{(n-1)!}{n!}a_1[/tex]

and with lots of cancellation, we end up with

[tex]a_n=\dfrac{a_1}n=\boxed{\dfrac2n}[/tex]

Answer:

Divide 2 by n.

Step-by-step explanation:

Answer:

  B.  135

Step-by-step explanation:

For ...

f(5) = 3·5^2 -5

   = 3·25 -5 = 75 -5 = 70

Then g(f(5)) is ...

  g(f(5)) = g(70) = 2·70 -5 = 140 -5

  g(f(5)) = 135 . . . . . matches choice B

Answer:

The probability that they have a mean height greater than 71.9 inches

P(  x⁻ ≥71.9) =  0.0022

Step-by-step explanation:

Explanation:-

Given mean of the Population μ= 70.9

Standard deviation of the Populationσ = 2.1

Given sample size 'n' =36

let x⁻ be the mean height

given  x⁻ =71.9 inches

[tex]Z=\frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z=\frac{71.9 -70.9}{\frac{2.1}{\sqrt{36} } } = \frac{1}{0.35} = 2.85[/tex]

The probability that they have a mean height greater than 71.9 inches

P(  x⁻ ≥71.9) = P(Z ≥ 2.85)

                    = 1 - P(Z≤ 2.85)

                   =  1 - ( 0.5 + A(2.85)

                   = 0.5 - A( 2.85)

                  = 0.5 - 0.4978

                  = 0.0022

The probability that they have a mean height greater than 71.9 inches

 P(  x⁻ ≥71.9) =  0.0022

Answer:

the answer is 0.0022

Step-by-step explanation:

Answer:

Check Explanation

Step-by-step explanation:

In finding the public's view on pollution, the researchers waited outside a car dealership they had randomly selected from a list of such establishments. They stopped every 10th person who came out of the dealership and asked whether he or she thought pollution was a serious problem.

A) The population

The population is the sum total of every member of the public whose opinions on pollution, the researchers are interested in.

B) The population parameter of interest

Since the researchers stopped every member of the sample to ask them whether they thought pollution was a serious problem or not, it follows that the population parameter of interest is the proportion of the population who think that pollution is a serious problem.

C) The sampling frame

The sampling frame is defined as the source material where the sample is drawn from. And for this question, the sampling frame is the population of people leaving car dealership establishments.

D) The sample

The sample is the set of people that were asked the question of whether population was a serious problem or not. The sample includes every 10th person that came out of the chosen car dealership establishments.

E) The sampling method

Note that

- In random sampling, each population member would have an equal chance of being surveyed.

- Stratified sampling divides the population into groups called strata. A sample is taken from some or all of these strata using either random, systematic, or convenience sampling.

- In systematic sampling, a particular number, n, is counted repeatedly and each of the nth member is picked to be sampled.

Hence, this stratified sampling method uses random sampling technique to pick the strata where the samples will be obtained from and systematic sampling is now used for the picking of the members of the sample.

F) Any potential sources of bias you can detect and any problems you see in generalizing to the population of interest.

This survey only limits the members of the sample to those who visit a car dealership, and this cuts out a large percentage of the total population of humans.

Mostly men visit car dealership establishments, Hence, women, children, old people are at a disadvantage as they do not all have an equal chance of being surveyed.

Infact, only a financial class of the population visits car dealership establishments, so, it would be very wrong with all of this bias to use the results of this surveyor generalize for the whole population of people.

Hope this Helps!!!

Answer:

The answer is around 27.63 seconds.

Step-by-step explanation:

1 km equals 1000 meters so we have to multiply 10,500 and 1,000 which would equal 10,500,000 km. 10,500,000 divided by 380,000 which is around 27.63 seconds.

Answer:

To the nearest hundredth of a percentage= 0.03

Step-by-step explanation:

Formula for compound interest

A= p(1+r/n)^nt

A= $330

P= $210

n = 356

t= 17

r = ?

330 = 210(1+r/356)^(356*17)

330 = 210(1+r/356)^(6052)

330/210 = (1+r/356)^6052

(6052√(330/210) - 1 )356 = r

(1.000074686-1)356= r

0.02658 = r

To the nearest hundredth of a percentage= 0.03

Answer:

2.66

Step-by-step explanation:

Answer:

0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Given to a woman.

Event B: Masters degree.

21% were master’s degrees

This means that [tex]P(B) = 0.21[/tex]

Women earned 40% of masters

This means that [tex]P(A|B) = 0.4[/tex]

Probability of the degree being given to a women:

52% of 76%, 40% of 21% and 22% of 3%. So

[tex]P(A) = 0.52*0.76 + 0.4*0.21 + 0.22*0.03 = 0.4858[/tex]

What is the probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman?

[tex]P(B|A) = \frac{0.21*0.4}{0.4858} = 0.1729[/tex]

0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman

Answer:

5^15

Step-by-step explanation:

(5^10)(5^5)= 5^10+5= 5^15

Answer: You can't. Read explanation.

Step-by-step explanation:

You can't subtract an expression from an equation. If you said something like subtract 8b-ab+7a from 3a-9ab+b that would work, but not here.

Let's just assume You mean it as 8b-ab-7a, then (3a-9ab+b)-(8b-ab-7a) = -8ab + 10a - 7b.

Hope that helped,

-sirswagger21

Answer:

By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean

By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean

95% of commuters in Boston has a commute time within 2 standard deviations of the mean

Empirical rule states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean.

Hence, 95% of commuters in Boston has a commute time within 2 standard deviations of the mean

Find out more on Empirical rule at: https://brainly.com/question/10093236

Answer:

The recoil velocity of the gun is [tex]0.72\,\,\frac{km}{h}[/tex]  and is pointing in opposite direction to the velocity of the bullet.

Step-by-step explanation:

Use conservation of linear momentum, which states that the momentum of the bullet (product of the bullet's mass times its speed) should equal in absolute value the momentum of the recoiling gun (its mass times its recoil velocity).

We also write the mass of the bullet in the same units as the mass of the gun (for example kilograms). Mass of the bullet = 0.010 kg

In mathematical terms, we have:

[tex]5\, kg * v= 0.01 \,kg\,* 360\,\frac{km}{h} \\v=\frac{0.01\,*360}{5} \,\,\frac{km}{h}\\v=0.72\,\,\frac{km}{h}[/tex]

Answer:

A

Step-by-step explanation:

It is not B because 7x^2 means multiplying the equation by seven. It isn't C because that would move the graph DOWN seven units. And it's not D because when it is in parenthesis like that, it means that it is a horizontal shift, not vertical.

Answer:

A. G(x) = [tex]x^2+7[/tex]

Step-by-step explanation:

→For the function to shift upwards 7 units, 7 must be added to the function, like so:

G(x) = [tex]x^2+7[/tex]

→F(x) + c (in this case is 7), cases a vertical shift and the function is moved "c," units. The graph would shift downwards if 7 was being subtracted.

This means the correct answer is A.

I apologize, I am stumped... I thought you would find either the centroid, circumcenter, or incenter of the triangle created but it didn't work quite right for me.

Answer:

 3x ≤ -6

Step-by-step explanation:

"At most" means "less than or equal to." If x represents the number, then you have ...

  (three) times (a number) (is at most) negative 6 . . . . . English

      3       ·         x                ≤           -6 . . . . . . . . . . . . . . . . Math

__

  3x ≤ -6

Answer:

3x ≤ -6

Step-by-step explanation:

Answer:

The sample size must be greater than 37 if we want to reject the null hypothesis.

Step-by-step explanation:

We are given that someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi.

Also, we are given a level of significance of 5%.

Let [tex]\mu[/tex] = mean breaking strength of their climbing rope

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 2,000 psi       {means that the mean breaking strength of their climbing rope is 2,000 psi}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 2,000 psi      {means that the mean breaking strength of their climbing rope is lower than 2,000 psi}

Now, the test statistics that we will use here is One-sample z-test statistics as we know about population standard deviation;

                         T.S.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = ample mean strength = 1,997.2956 psi

            [tex]\sigma[/tex] = population standard devaition = 10 psi

            n = sample size

Now, at the 5% level of significance, the z table gives a critical value of -1.645 for the left-tailed test.

So, to reject our null hypothesis our test statistics must be less than -1.645 as only then we have sufficient evidence to reject our null hypothesis.

SO,  T.S. < -1.645   {then reject null hypothesis}

         [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < -1.645[/tex]

         [tex]\frac{1,997.2956-2,000}{\frac{10}{\sqrt{n} } } < -1.645[/tex]

         [tex](\frac{1,997.2956-2,000}{10}) \times {\sqrt{n} } } < -1.645[/tex]

          [tex]-0.27044 \times \sqrt{n}< -1.645[/tex]

               [tex]\sqrt{n}> \frac{-1.645}{-0.27044}[/tex]

                 [tex]\sqrt{n}>6.083[/tex]

                  n > 36.99 ≈ 37.

SO, the sample size must be greater than 37 if we want to reject the null hypothesis.

Answer:

[tex]\frac{\pi x^3}{3}[/tex]

Step-by-step explanation:

[tex]V=\pi r^2h\frac{1}{3}[/tex]

[tex]V=\pi x^2x\frac{1}{3}[/tex]

[tex]V=\pi x^3\frac{1}{3}[/tex]

[tex]V=\frac{\pi x^3}{3}[/tex]

[tex]V=1.047198x^3[/tex]

Answer:

Step-by-step explanation:

1/12 pi x ^3

Answer:

a) The equation of Z and C is Z =K C

b) K = 2

Step-by-step explanation:

Explanation :-

Given data Z is directly proportional to C

              ⇒   Z ∝ C

               ⇒  Z = K C

The equation of relating Z and C    

               Z = K C

Given Z = 20 and C =10

              20 = K ( 10)

          ⇒ K = 2

Answer:

The slope of AB is

different than the

slope of BC.

Step-by-step explanation:

Answer:

81%

Step-by-step explanation:

22+5=27

22/27

Answer:

113.09 hope this helps

Step-by-step explanation:

Answer:

B

The mode is 11 and 3

The Median is 10

The mean is 12

Answer:

The number of students reporting readings between 87 g and 89 g is 61

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 88g

Standard deviation = 1g

Percentage of students reporting readings between 87 g and 89 g

87 = 88-1

So 87 is one standard deviation below the mean.

89 = 88+1

So 89 is one standard deviation above the mean.

By the Empirical Rule, 68% of students are reporting readings between 87 g and 89 g.

Out of 90 students:

0.68*90 = 61.2

Rounding to the nearest whole number:

The number of students reporting readings between 87 g and 89 g is 61

Answer:

C is the correct answer.

Step-by-step explanation:

The reason it is C is because pi/the symbol on top is irrational.

Hope you have a good rest of your day :)

Answer:

An acute angle is open

Step-by-step explanation:

An acute angle is an angle that is less than [tex]90^{0}[/tex]. Two or more acute angles are set to be complementary if their sum equals a right angle.

Clara's diagram involves two acute angles JLK and KLM with both sharing the side LK.

If the acute angles are complementary angles, then JLM would be a right angle.

If the acute angles are not complementary angles, then JLM would be less than a right angle.

So the appropriate choice to select is an acute angle is open. Which implies that JLM may be a right angle or not depending on the degrees of the acute angles involved.

Answer:

the loan was 1000

Step-by-step explanation:

Take the tuition and multiply by 5/6

1200 *5/6

1200/6 *5

200 *5

1000

Answer:

$1000

Step-by-step explanation:

In order to find 5/6 of the tuition, we just need to multiply the 2 values together.

5/6*1200

Note that 1200 = 1200/1

5/6*1200/1

When multiplying fractions, we can multiply the numerators together, and the denominators together.

5*1200/6*1

6000/6

Divide.

1000

Therefore, the loan was $1000.

Answer: To increase an amount by 7%, you would want to use 1.07 as the multiplier. To decrease it, you would use 0.93

Step-by-step explanation:

Answer:

There are many. Two examples are

[tex]f(x) = x, \\f(x) = x^3[/tex]

Step-by-step explanation:

There are many examples. The simplest is

1 -

[tex]f(x) = x[/tex]

It is trivial that

[tex]\text{if \,\,\,\,} f(x) = f(y) \,\,\,\,\,\text{then} \,\,\,\,\, x=y[/tex]

2 -

[tex]f(x) = x^3[/tex]

That function is injective as well.

[tex]\text{if \,\,\,\,} x^3 = y^3 \,\,\,\,\,\text{then} \,\,\,\,\, x=y[/tex]

An example of a function that is NOT injective is

[tex]f(x) = x^2[/tex]

Notice that

[tex]f(-2) = (-2)^2 = 2^2 = 4[/tex]

Answer:

Aisha is shorter than 43 inches.

Step-by-step explanation:

[tex]x+5=48[/tex]

[tex]x=48-5[/tex]

[tex]x=43[/tex]

[tex]x >43[/tex]

Answer:

The answer is B!

Step-by-step explanation:

Test taking! <3

Answer:

The best data collection method or sampling method to provide an unbiased sample is the random sampling method.

Step-by-step explanation:

There are 5 popular known sampling methods or data collection methods.

1) Random Sampling

In random sampling, each member of the population would have an equal chance of being surveyed. One of the best ways to use random sampling is to give all the members of the population numbers and then use computer to generate random numbers and pick the members of the population with those random numbers.

2) Systematic sampling is easier than random sampling. In systematic sampling, a particular number, n, is counted repeatedly and each of the nth member is picked to be sampled.

3) Convenience Sampling

This is the worst sampling technique. It is also the easiest. In Convenience sampling, the surveyor just picks the first set of members of the population that they find and surveys.

4) Stratified Sampling

Stratified sampling divides the population into groups called strata. A sample is taken from each of these strata using either random, systematic, or convenience sampling.

5) Cluster sampling

Cluster Sampling divides the population into groups which are called clusters or blocks. The clusters are selected randomly, and some members or every element/member in the selected clusters is surveyed.

Hope this Helps!!!

Answer:

Option C.

Step-by-step explanation:

The given logarithmic equation is

[tex]\log_2(x+11)=4[/tex]

It can be written as

[tex](x+11)=2^4[/tex]     [tex][\because log_ax=y\Leftrightarrow x=a^y][/tex]

[tex]x+11=16[/tex]

[tex]x=5[/tex]

Now, to check whether [tex]x=5[/tex] is a true solution or not. Substitute [tex]x=5[/tex] in the LHS of given equation.

[tex]LHS=\log_2(5+11)[/tex]

[tex]LHS=\log_2(16)[/tex]

[tex]LHS=\log_22^4[/tex]

[tex]LHS=4[/tex]     [tex][\because log_aa^x=x][/tex]

[tex]LHS=RHS[/tex]

Hence, [tex]x=5[/tex] is a true solution because [tex]\log_2(16)=4[/tex].

Therefore, the correct option is C.

Answer:

C on edge2021

Step-by-step explanation: