Employees at a company produced refrigerators on three shifts. Each shift recorded their quality stats below. A unit was considered defective if it at least one part was assembled wrong or was missing. Management believes that quality depends on the the shift it was produced. Test the claim that shifts are independent of quality using chi-square at alpha = 0.05. SHOW YOUR WORK
Answers
Answer:
Step-by-step explanation:
Hello!
So in the refrigerator factory there are three shifts. Each shift records their quality based on the quantity of defective and working parts assembled.
Using a Chi-Square test of independence you have to test the claim that quality and shifts are independent.
The hypotheses are:
H₀: The variables are independent.
H₁: The variables are not independent.
α: 0.05
[tex]X^2= sum\frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~X_{(r-1)(c-1)}[/tex]
r= total number of rows
c= total number of columns
i= 1, 2 (categories in rows)
j=1, 2, 3 (categories in columns)
To calculate the statistic you have to calculate the expected frequencies for each category:
[tex]E_{ij}= \frac{O_{i.}*O_{.j}}{n}[/tex]
[tex]O_{i.}[/tex] Represents the marginal value of the i-row
[tex]O_{.j}[/tex] Represents the marginal value of the j-column
[tex]E_{11}= \frac{O_{1.}*O_{.1}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{12}= \frac{O_{1.}*O_{.2}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{13}= \frac{O_{1.}*O_{.3}}{n}= \frac{21*40}{120}= 7[/tex]
[tex]E_{21}= \frac{O_{2.}*O_{.1}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]E_{22}= \frac{O_{2.}*O_{.2}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]E_{23}= \frac{O_{2.}*O_{.3}}{n}= \frac{99*40}{120}= 33[/tex]
[tex]X^2_{H_0}= \frac{(7-7)^2}{7} + \frac{(5-7)^2}{7} + \frac{(9-7)^2}{7} + \frac{(33-33)^2}{33} + \frac{(35-33)^2}{33} + \frac{(31-33)^2}{33} = 1.385= 1.34[/tex]
Using the critical value approach, the rejection region for this test is one-tailed to the right, the critical value is:
[tex]X^2_{(c-1)(r-1);1-\alpha }= X^2_{2; 0.95}= 5.991[/tex]
Decision rule:
If [tex]X^2_{H_0}[/tex] ≥ 5.991, reject the null hypothesis.
If [tex]X^2_{H_0}[/tex] < 5.991, do not reject the null hypothesis.
The value of the statistic is less than the critical value, the decision is to not reject the null hypothesis.
At 5% significance level, you can conclude that the shift the pieces were assembled and the quality of said pieces are independent.
I hope this helps!
Related Questions
lucy buys 3 liters of apple juice. How many millilitres of apple juice does she buy?
*please help*
Answers
Answer:
3000 milliliters
Step-by-step explanation:
1liter contains 1000militers
3liters contain (3*1000)militers
Answer:
3000 millilitres
Step-by-step explanation:
since 1 litre = 1000 millimetres
3 litres will be equal to 1000 x 3 = 3000 ml
Solve for n.
11(n – 1) + 35 = 3n
n = –6
n = –3
n = 3
n = 6
Answers
11n+24=3n
11n-3n=-24
8n=-24
n=-24/8
n=-3
Answer:
[tex]n = - 3[/tex]
Second answer is correct
Step-by-step explanation:
[tex]11(n - 1) + 35 = 3n \\ 11n - 11 + 35 = 3n \\ 11n - 3n = 11 - 35 \\ 8n = - 24 \\ \frac{8n}{8} = \frac{ - 24}{8} \\ n = - 3[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
How many days are there in 12 weeks? Use the following information to convert this time to days. 1 week = 7 days
Answers
Answer:
84days
Step-by-step explanation:
1 week = 7days =>12 weeks = 12×7 = 84days
Answer:
84 days are in 12 weeks
Step-by-step explanation:
1 week = 7 days
4 weeks = 28 days
So 28 + 28 + 28 = 84 days
A 2-pack of scented candles costs $0.95. What is the unit price, rounded to the nearest cent?i mark the 1st answer brainliest
Answers
Step-by-step explanation:
Cost of 2 pack = 0.95
Cost of 1 pack = 0.95 ÷ 2 = 0.475
Unit price = 0.475
What is simplified form of the fifth square root of x times the fifth square root of x times the fifth square root of x times the fifth square root of x
Answers
Answer: This was a bit hard to understand, x times the 5th root of x
Step-by-step explanation:
When you multiply square roots of the same root and inside value, they essentially get rid of the square roots. So the first two terms boil down to just x. Then multiply x by the 5th root of x to get:
[tex]x\sqrt[5]{x}[/tex]
Answer:
[tex]x[/tex]
Step-by-step explanation:
Apply exponent rules.
[tex]\sqrt{x} =x^\frac{1}{2}\\\:a^b\times \:a^c=a^{b+c}[/tex]
[tex]\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x} \times\sqrt[5]{x}[/tex]
[tex]x^{\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}}[/tex]
[tex]x^1[/tex]
Find the area of the smaller sector.
Round to the nearest tenth.
Help needed fast
Answers
Answer:
About 22.2 square feet
Step-by-step explanation:
First, you need to find the area of the full circle. The area of a circle is \pi r^2, which in this case is:
[tex]\pi r^2 = \pi \cdot 7.13^2\approx 159.628[/tex]
Now, since the sector is only 50 out of the total 360 degrees in a circle, you need to multiply this value by 50/360, which yields and area of about 22.2 square feet. Hope this helps!
Divide £2.28 btw eve and amelie in the ratio 9:5 give your answer to the nearest penny Eve gets ? And amelie gets ?
Answers
Answer:
Eve gets 1.47 and Amelie gets 0.81
Step-by-step explanation:
the ratio is 9 to 5 so we can say 9x + 5x=2.28
14x=2.28
x=0.16
so eve gets 9x = 9(2.28/14) = 1.47
and amelie gets 5x = 5(2.28/14) = 0.81
Solve for x. e^x - e ^ -x / e^x + e ^-x = t
Answers
Answer:
D
Step-by-step explanation:
(eˣ − e⁻ˣ) / (eˣ + e⁻ˣ) = t
Multiply by eˣ/eˣ.
(e²ˣ − 1) / (e²ˣ + 1) = t
Solve for e²ˣ.
e²ˣ − 1 = (e²ˣ + 1) t
e²ˣ − 1 = e²ˣ t + t
e²ˣ = 1 + e²ˣ t + t
e²ˣ − e²ˣ t = 1 + t
e²ˣ (1 − t) = 1 + t
e²ˣ = (1 + t) / (1 − t)
Solve for x.
2x = ln[(1 + t) / (1 − t)]
x = ½ ln[(1 + t) / (1 − t)]
Use log rule.
x = ln(√[(1 + t) / (1 − t)])
A box is a cuboid with dimensions 28cm by 15cm by 20cm all measured to the nearest centimetre.
Disc cases are cuboid which measure 1.5 by 14.2 cm by 19.3 cm all measure to the nearest millimetre. Show that 17 disc cases, stacked as shown, will definitely fit the box
Answers
Answer:
The 17 disc cases would definitely fit into the box.
Step-by-step explanation:
The given cuboid box has the dimensions 28cm by 15cm by 20cm.
Disc cases are cuboid with dimensions 1.5cm by 14.2cm by 19.3cm.
volume of a cuboid = length × width × height
Volume of the box = 28 × 15 × 20
= 8400 cubic centimeters
Volume of each disc case = 1.5 × 14.2 × 19.3
= 411.09 cubic centimeters
When the 17 disc cases are stacked it would have a volume.
The volume of 17 disc cases = 17 × volume of a case
= 17 × 411.09
= 6988.53 cubic centimeters
Thus comparing the volume for 17 disc cases and that of the cuboid box, the disc cases would definitely fit into the box.
i.e = [tex]\frac{volume of box}{volume of 17 disc cases}[/tex]
= [tex]\frac{8400}{6988.53}[/tex]
= 1.20
Answer:
Step-by-step explanation:
27.5×14.5×19.5 =7775.625 cm³
1.55 x 14.25 x 19.35=427.393125
427.393125 x 17=7265.683
7775.625>7265.683
19.5x27.5x14.5=7775.625
1.45x14.15x19.25=394.961875
394.961875x17=6714.35
7775.63>6714.35
1.55x17=26.35
27.5>26.35
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 258.7 and a standard deviation of 63.5. (All units are 1000 cells/muL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 68.2 and 449.2? b. What is the approximate percentage of women with platelet counts between 195.2 and 322.2?
Answers
Answer:
a) [tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]
And from the empirical rule we know that this probability is 0.997 or 99.7%
b)[tex] P(195.2 <X<322.2)[/tex]
Using the z score we have:
[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]
[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]
And within one deviation from the mean we have 68% of the values
Step-by-step explanation:
For this case we defien the random variable of interest X as "blood platelet counts" and we know the following parameters:
[tex] \mu = 258.7, \sigma =63.5[/tex]
Part a
We can use the z score formula given by:
[tex] z =\frac{\bar X -\mu}{\sigma}[/tex]
And we want this probability:
[tex]P( \mu -3\sigma <X< \mu +3\sigma)[/tex]
And from the empirical rule we know that this probability is 0.997 or 99.7%
Part b
For this case we want this probability:
[tex] P(195.2 <X<322.2)[/tex]
Using the z score we have:
[tex] z = \frac{322.2 -258.7}{63.5}= 1[/tex]
[tex] z = \frac{195.2 -258.7}{63.5}= -1[/tex]
And within one deviation from the mean we have 68% of the values
A random sample of 1,000 StatCrunchU students contains 598 female and 402 males. We analyze responses to the question, "What is the total amount (in dollars) of your student loans to date?" Two sample T confidence interval: μ 1: Mean of Loans where Gender="Female" μ 2: Mean of Loans where Gender="Male" μ 1 − μ 2: Difference between two means (without pooled variances) 95% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit μ 1 − μ 2 516.74334 368.41116 907.34739 -206.29374 1239.7804 What can we conclude from the 95% confidence interval? Check all that apply. Group of answer choices
Answers
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
Here, we have,
From the provided 95% confidence interval, we can make the following conclusions:
The point estimate of the difference between the mean student loans for females and males is 516.74334 dollars.
The standard error of the difference between the means is 368.41116 dollars.
The degrees of freedom (DF) associated with the confidence interval is 907.34739.
The lower limit of the confidence interval is -206.29374 dollars.
The upper limit of the confidence interval is 1239.7804 dollars.
The confidence interval does not contain zero.
Since zero is not within the interval, we can conclude that the difference between the mean student loans for females and males is statistically significant at the 95% confidence level.
Based on the information given, these are the conclusions we can draw from the 95% confidence interval.
Learn more about confidence interval here:
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The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Based on the 95% confidence interval provided for the difference in means between the loans of female and male StatCrunchU students, we can draw the following conclusions:
The sample difference in means is 516.74334.
The standard error of the difference is 368.41116.
The degrees of freedom (DF) for the analysis is 907.34739.
The lower limit of the confidence interval is -206.29374.
The upper limit of the confidence interval is 1239.7804.
Therefore, we can conclude the following:
The estimated difference in the mean student loans between females and males is 516.74334.
There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.
Note: Since the confidence interval includes both positive and negative values, we cannot conclude with certainty whether there is a significant difference or not in the mean student loans between females and males. The confidence interval suggests that the difference could be positive, negative, or even zero.
For more such questions on difference in the mean
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1960 were polled. 279 of them preferred Rock and Roll. What is the % of these students?
Answers
Answer:
14.2% students
Step-by-step explanation:
279 / 1960 = 0.142
0.142 x 100% = 14.2 %
A linear track begins at 0 meters and has a total distance of 100 meters to the finish line. Juliet starts at the 100 meter mark while practicing for a race. After running 45 meters how far is she from the beginning of the track?
Answers
Answer:
It’s D, 55.
Step-by-step explanation:
After running 45 meters, Juliet runs 55 meters from the beginning of the track
Translate the phrase into a variable expression. Use the letter d to name the variable. If necessary use the asterisk for multiplication and the slash for division The numbers of dollars Paul owes plus 16..
Answers
Answer:
This can be written as d + 16 because plus means addition.
Triangle ABC has been dilated about point A by a scale factor of One-third.
Triangle A B C. Side A C has a length of 39, side A B is 30, side C B is 48. Triangle A prime B prime C prime.
What are the lengths, in units, of the three sides of Triangle A prime B prime C prime?
Answers
Answer:
10,16,13
Step-by-step explanation:
got that right
The lengths of the sides of the triangle after the dilation is 13 , 10 and 16 respectively
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the triangle be represented as ABC
Now , the dilated triangle is represented as A'B'C'
The dilation scale factor is d = 1/3
The measure of side AC = 39
The measure of side AB = 30
The measure of side BC = 48
Now , after the dilation of 1/3 , we get
The measure of side A'C' = 39 ( 1/3 ) = 13
The measure of side A'B' = 30 ( 1/3 ) = 10
The measure of side B'C' = 48 ( 1/3 ) = 16
Hence , the dilation triangle is having lengths 13 , 10 and 16
To learn more about dilation click :
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find the slope of the line through points 8,2 and -1,-4
Answers
Answer:
2/3
Step-by-step explanation:
We can find the slope by using the slope formula
m= (y2-y1)/(x2-x1)
= (-4-2)/(-1-8)
= -6/ -9
= 2/3
A survey asks teachers and students whether they would like the new school
mascot to be a shark or a moose. This table shows the results. Which
statement is true?
Answers
Help asap giving branlist!!
Answers
Answer: Thr amount spent to manufacture each radio.
Step-by-step explanation: I put two and two together...lol...plz brainlest.
Answer:
The amount spent to manufacture each radio.
Step-by-step explanation:
125 is the start up cost and each radio costs 5.25 to make.
What is the value of m squared minus 2 m n + n squared for m = negative 2 and n = 4?
Answers
-4-2×-2×64
-4+4×64
-4+256
=252
Answer: (36)
hope this helps you have a wonderful day
Step-by-step explanation:
simplify 8-(3a+8)=
havent done these in a while so...
Answers
Answer:
3
Step-by-step explanation:
8-(3a+8)
8-(11a)
8-11a
a=11-8
a=3
Answer:
0
Step-by-step explanation:
8-(3a+8)=0
8-3a-8=0
-3a=0
a=0
A spherical balloon is inflated with gas at a rate of 600 cubic centimeters per minute.
(a) Find the rates of change of the radius when r = 50 centimeters and r = 85 centimeters.
r = 50 ? cm/min
r = 85 ? cm/min
(b) Explain why the rate of change of the radius of the sphere is not constant even though dv/dt is constant.
A.) dr/dt as a function runs parallel to the volume function, which is not linear
B.) The rate of change of the radius is a linear relationship whose slope is dV/dt
C.) The rate of change of the radius is a cubic relationship.
D.) The volume only appears constant; it is actually a rational relationship.
E.) dr/dt depends on r2, not simply r.
Answers
A store has 80 modems in its inventory, 30 coming from Source A and the remainder from Source B. Of the modems from Source A, 20% are defective. Of the modems from Source B, 8% are defective. Calculate the probability that exactly two out of a sample of five modems selected without replacement from the store’s inventory are defective.
Answers
Answer:
0.102
Step-by-step explanation:
The number of defective modems in the inventory is 20% * 30 + 8% * 0.50 =10 (out of 80)
Note that the number of defectives in the inventory is fixed i.e. we are told that there is 1/8 probability that a modem in the inventory is defective, but rather that exactly 1/8 of all modems are defective.
The probability that exactly two modems in a random sample of five are defective is :
(10↓2)(70↓3) / (80↓5) = 0.102
simplify 2(f^4)^2/8f^12
Answers
Answer:
Step-by-step explanation:
2(f^4)^2/8(f^12)
2/8= 1/4
f^16/f^12
f^(16-12)= f^4
f^4/4 is the solution
I am divisible by 3.
I am an even number.
I am the missing number
in 48/x=8.
Who am I?
Answers
Answer:
You are 6
Step-by-step explanation:
8×6=48 and 6/3=2
6 is even and fits in all of these areas.
Hope this helps.
Mark brainliest if correct.
A taxi company manager is trying to decide whether the use of radial tires instead of regular belted tires improves fuel economy. Twelve cars were equipped with radial tires and driven over a prescribed test course. Without changing drivers, the same cars were then equipped with regular belted tires and driven once again over the test course. The gasoline consumption, in kilometers per liter, was recorded as follows:
Car Radial-Tires Belted-Tires
1 4.2 4.1
2 4.7 4.9
3 6.6 6.2
4 7.0 6.9
5 6.7 6.8
6 4.5 4.4
7 5.7 5.7
8 6.0 5.8
9 7.4 6.9
10 4.9 4.7
11 6.1 6.0
12 5.2 4.9
A two-sample t-test was used to compare the mean kilometers per liter for the two types of tires using a .05 level of significance. The resulting p-value was .0152.
State the null and alternate hypotheses, state whether the null hypothesis should be rejected or not rejected and your reason for that conclusion, state the meaning of that conclusion specifically in terms of the problem being studied.
Answers
Answer:
Step-by-step explanation:
Corresponding gasoline consumption when radial tires is used and gasoline consumption when regular belted tires is used form matched pairs.
The data for the test are the differences between the gasoline consumption when radial tires is used and gasoline consumption when regular belted tires is used.
μd = the gasoline consumption when radial tires is used minus the gasoline consumption when regular belted tires is used.
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The resulting p-value was .0152.
Since alpha, 0.05 > than the p value, 0.0152, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the gasoline consumption when regular belted tires is used is higher than the gasoline consumption when radial tires is used.
Explain how to find the range of a data set. Choose the correct answer below. A. The range is found by subtracting the first data entry from the last data entry. B. The range is found by adding the first and last data entries. C. The range is found by subtracting the minimum data entry from the maximum data entry. D. The range is found by adding the minimum and maximum data entries.
Answers
Answer:
C
Step-by-step explanation:
The range of a data set is the difference between the biggest and smallest values, so to find it, you just subtract the minimum from the maximum.
Carole's age is five times Joe's age. The sum of their ages is 18. How old are Carole and Joe?
Answers
Answer:
Carole is 15
Joe is 3
Step-by-step explanation:
Carole's age is 15
Joes age is 3
3*5=15
15+3=18
Answer:
Carole = 15 Yrs
Joe = 3 Yrs
Step-by-step explanation:
15/5 =3
15+3 =18
Sry for the short explanation. Hope this helps!
The average score Josie had in 6 subjects is 72 and her average score after 2 additional subjects were added is 74.25. If she scored 80 in the 7th subject, what was her score in the 8th subject correct to the nearest whole number?
Answers
Answer:82
Step-by-step explanation:
a+b+c+d+e+f/6=72
a+b+c+d+e+f=6*72
a+b+c+d+e+f=432
a+b+c+d+e+f+g+h/8=74.25
a+b+c+d+e+f+g+h=594
g=80
h=?
432+80+h=594
512+h=594
h=82
hope it helps brainleast plz...
A spherical gemstone just fits inside a plastic cube with edges 12cm. a) calculate the volume of gemstone, to the nearest cubic centimeter. b) how much empty space is there.
Answers
Answer:
a) (V) = 904.78 of a sphere = 288pi diameter = 12
(V) = 1728cm^3 of a cube = face diagonal = 16.9cm
b) Difference Volume = 1728-904.78 = 823.22cm^3
Step-by-step explanation:
To find volume of an inscribed sphere within a square cube
We use 4 π/3 * r^3 for the equation
As Radius = 6 = 6cm this is the only thing plugged into the equation to create a division first then a multiplication square of radius and then a multiplication. 4pi /3 * 6^3
r^3 = 216
4pi/3 = 4.18
4.18 * 216 = 904.78
This means the answer is 288 pi cm^3.
Answer:
volume of gemstone = 905 cm^3
volume of empty space = 823 cm^3
Step-by-step explanation:
volume of cube = s^3, where s = length of edge
volume of sphere = (4/3)(pi)r^3, where r = radius of sphere
The cube has a 12-cm edge. The sphere fits tightly inside the cube, so the diameter, d, of the sphere is 12 cm. The radius is half the diameter, so radius = r = diameter/2 = 12 cm/2 = 6 cm.
a)
volume of sphere = (4/3)(pi)r^3
volume of sphere = (4/3)(3.14159)(6 cm)^3
volume of sphere = 905 cm^3
b)
The empty space is the difference between the volume of the cube and the volume of the sphere.
volume of cube = s^3
volume of cube = (12 cm)^3
volume of cube = 1728 cm^3
empty space = volume of cube - volume of sphere
empty space = 1728 cm^3 - 905 cm^3
empty space = 823 cm^3
what are the answers to the following quadratic equation:
x^2-4x-12
Answers
Answer:
6 and -2
Step-by-step explanation:
x^2-4x-12
set up equal to zero
x^2-4x-12=0
lets factor:
(x-6)(x+2)=0
x-6=0
x=6
or
x+2=0
x=-2
Answer:
x=6 x=-2
Step-by-step explanation:
x^2-4x-12 = 0
Factor
What two numbers multiply to -12 and add to -4
-6*2 = -12
-6+2 = -4
(x-6)(x+2) =0
Using the zero product property
(x-6) =0 x+2 = 0
x=6 x=-2
