Instructions for Students:

Answer ONLY part a in Question 4. Questions carry equal marks. You have to show the work to earn marks. Answers must be uploaded on Moodle under Assignment II.

Unless stated, you can either use Excel or do calculations by hand to answer each question. However, if Excel is used to answer any question, the original Excel file must be uploaded too.

You can either create a Word or Excel file to answer questions, or write your answers on

paper and take a photo of it.

Assignment:Assignment II - BUQU1230 1. The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.68 inches and a standard

deviation of 0.04 inch. A random sample of 10 tennis balls is selected. Complete parts (a) through (d) below.a.What is the sampling distribution of the mean?

Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will be the uniform distribution.

Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will also be approximately normal.

Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 cannot be found.

Because the population diameter of tennis balls is approximately normally distributed, the sampling distribution of samples of size 10 will not be approximately normal.

b.What is the probability that the sample mean is less than 2.65 inches? P(X < 2.65) =

(Round to four decimal places as needed.) c.What is the probability that the sample mean is between 2.66 and 2.69 inches?

P(2.66

d.The probability is 57% that the sample mean will be between what two values symmetrically distributed around the population mean?

The lower bound isinches. The upper bound isinches. (Round to two decimal places as needed.)

2. The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,515 hours. The population standard deviation is 92 hours. A random sample of 64 light bulbs indicates a sample mean life of 7,492 hours. a.At the 0.05 level of significance, is there evidence that the mean life is different from 7,515 hours?

b.Compute the p-value and interpret its meaning. c.Construct a 95% confidence interval estimate of the population mean life of the light bulbs.d.Compare the results of (a) and (c). What conclusions do you reach?

a.Let be the population mean. Determine the null hypothesis, H0, and the alternative hypothesis, H1. H0: =

H1: What is the test statistic? ZSTAT= (Round to two decimal places as needed.) What is/are the critical value(s)?

(Round to two decimal places as needed. Use a comma to separate answers as needed.) What is the final conclusion?

Reject H0. There is not sufficient evidence to prove that the mean life is different from 7,515 hours.

Reject H0. There is sufficient evidence to prove that the mean life is different from 7,515 hours.

Fail to reject H0. There is sufficient evidence to prove that the mean life is different from 7,515 hours.

Fail to reject H0. There is not sufficient evidence to prove that the mean life is different from 7,515 hours.

b.What is the p-value? (Round to three decimal places as needed.)

Interpret the meaning of the p-value. Choose the correct answer below.

Reject H0. There is not sufficient evidence to prove that the mean life is different from 7,515 hours.

Fail to reject H0. There is sufficient evidence to prove that the mean life is different from 7,515 hours.

Fail to reject H0. There is not sufficient evidence to prove that the mean life is different from 7,515 hours.

Reject H0. There is sufficient evidence to prove that the mean life is different from 7,515 hours.

c.Construct a 95% confidence interval estimate of the population mean life of the light bulbs. (Round to one decimal place as needed.)

d.Compare the results of (a) and (c). What conclusions do you reach? A.The results of (a) and (c) are the same: there is sufficient evidence to prove that the mean life

is different from 7,515 hours.

The results of (a) and (c) are the same: there is not sufficient evidence to prove that the mean

life is different from 7,515 hours.

The results of (a) and (c) are not the same: there is not sufficient evidence to prove that the mean life is different from 7,515 hours.

The results of (a) and (c) are not the same: there is sufficient evidence to prove that the mean life is different from 7,515 hours.

3. A recent study found that 61 children who watched a commercial for potato chips featuring a celebrity endorser ate a mean of 39 grams of potato chips as compared to a mean of 26 grams for 51 children who watched a commercial for an alternative food snack. Suppose that the sample standard deviation for the children who watched the celebrity-endorsed commercial was 21.4 grams and the sample standard deviation for the children who watched the alternative food snack commercial was 12.9 grams. Complete parts (a) through (c) below.

a.Assuming that the population variances are equal and = 0.05, is there evidence that the mean amount of potato chips eaten was significantly higher for the children who watched the celebrity-endorsed commercial?

Let population 1 be the weights of potato chips eaten by children who watched the celebrity-endorsed commercial and let population 2 be the weights of potato chips eaten by children who watched the alternative food snack commercial. What are the correct null and alternative hypotheses?

A. C.

What istSTAT=

What is p-value What is

A. B. C. D.

H0:120H1:12>0

H0:120H1:12<0

B.H0:12=0H1:120

D.H0:120H1:12=0

the test statistic? (Round to two decimal places as needed.)

the corresponding p-value? =(Round to three decimal places as needed.)

the correct conclusion?

Reject H0. There is insufficient evidence that the mean amount of potato chips eaten was significantly higher for children who watched the celebrity-endorsed commercial.

Do not reject H0. There is sufficient evidence that the mean amount of potato chips eaten was significantly higher for children who watched the celebrity-endorsed commercial.

Reject H0. There is sufficient evidence that the mean amount of potato chips eaten was significantly higher for children who watched the celebrity-endorsed commercial.

Do not reject H0. There is insufficient evidence that the mean amount of potato chips eaten was significantly higher for children who watched the celebrity-endorsed commercial.

b.Assuming that the population variances are equal, construct a 95% confidence interval estimate of the difference between the mean amount of potato chips eaten by the children who watched the celebrity-endorsed commercial and

children who watched the alternative food snack commercial.

12 (Type integers or decimals rounded to two decimal places as needed.)

c.Compare and discuss the results of (a) and (b).

The confidence interval in part (b) does not contain 0, which agrees with the decision made in

part (a) to reject the null hypothesis.

The confidence interval in part (b) contains 0, which agrees with the decision made in part (a) to not reject the null hypothesis.

The confidence interval in part (b) contains 0, which does not agree with the decision made in part (a) to reject the null hypothesis.

The confidence interval in part (b) does not contain 0, which does not agree with the decision made in part (a) to not reject the null hypothesis.

12

4. A survey of six accounting firms in the Capital Region, Great Lakes, Mid-Atlantic, and Northeast regions included the number of partners in the firm. This information is included in the data table below. Complete (a) and (b) below. 1Click on the icon to view the data table. 2Click on the icon to view a partial table of critical values of the Studentized Range, Q.

a.At the 0.05 level of significance, is there evidence of a difference among the Capital, Great Lakes, Mid-Atlantic, and Northeast region accounting firms with respect to the mean number of partners?

Determine the hypotheses. Choose the correct answer below.

A.H0:1=2==6H1: Not alljare equal

(where j = 1,2,...,6)

C.H0:1=2==4H1:124

B.H0:1=2==4H1: Not alljare equal (where j = 1,2,...,4)

D.H0:1=2==6H1:126

Find the test statistic. FSTAT= (Type an integer or decimal rounded to two decimal places as needed.) Determine the critical value. F = (Type an integer or decimal rounded to two decimal places as needed.) Reach a decision.

(1) H0. There is (2)evidence of a difference in the mean number of partners in the accounting firms.

b.If appropriate, determine which regions differ in mean number of partners. Use a table of critical values of the Studentized range to find Q for = 0.05.

Q0.05=(Type an integer or a decimal rounded to two decimal places as needed.) Is there significant evidence that the Capital and the Great Lakes differ?

Yes because the absolute difference in the sample means is less than the critical range.

Yes because the absolute difference in the sample means is greater than the critical range.

No because the absolute difference in the sample means is less than the critical range.

No because the absolute difference in the sample means is greater than the critical range.

It is not appropriate to test which brands differ in mean strength.

Is there significant evidence that the Capital and the Mid-Atlantic differ?

No because the absolute difference in the sample means is greater than the critical range.

Yes because the absolute difference in the sample means is less than the critical range.

No because the absolute difference in the sample means is less than the critical range.

Yes because the absolute difference in the sample means is greater than the critical range.

It is not appropriate to test which brands differ in mean strength.

Is there significant evidence that the Capital and the Northeast differ? A.No because the absolute difference in the sample means is less than the critical range.

No because the absolute difference in the sample means is greater than the critical range.

Yes because the absolute difference in the sample means is less than the critical range.

Yes because the absolute difference in the sample means is greater than the critical range.

It is not appropriate to test which brands differ in mean strength.

Is there significant evidence that the Great Lakes and the Mid-Atlantic differ?

No because the absolute difference in the sample means is greater than the critical range.

No because the absolute difference in the sample means is less than the critical range.

Yes because the absolute difference in the sample means is less than the critical range.

Yes because the absolute difference in the sample means is greater than the critical range.

It is not appropriate to test which brands differ in mean strength.

Is there significant evidence that the Great Lakes and the Northeast differ?

No because the absolute difference in the sample means is greater than the critical range.

No because the absolute difference in the sample means is less than the critical range.

Yes because the absolute difference in the sample means is greater than the critical range.

Yes because the absolute difference in the sample means is less than the critical range.

It is not appropriate to test which brands differ in mean strength.

Is there significant evidence that the Mid-Atlantic and the Northeast differ?

No because the absolute difference in the sample means is less than the critical range.

No because the absolute difference in the sample means is greater than the critical range.

Yes because the absolute difference in the sample means is less than the critical range.

Yes because the absolute difference in the sample means is greater than the critical range.

It is not appropriate to test which brands differ in mean strength.

1: Number of partners in six accounting firms

Capital Region26 13 20 17 38 12

Number of Partners

Great Mid-Atlantic Northeast Lakes

50 113 15 86 158 22 83 16 24 66 91 27

110 122 21 38 58 20

2: Critical values of the Studentized Range, Q

(1)Do not reject(2)sufficient Reject insufficient

5. An agent for a real estate company wanted to predict the monthly rent for apartments based on the size of the apartment. The data for a sample of 25 apartments is available below. Perform a t test for the slope to determine if a significant linear relationship between the size and the rent exists.

a.At the 0.05 level of significance, is there evidence of a linear relationship between the size of the apartment and the monthly rent? b.Construct a 95% confidence interval estimate of the population slope,1. 3Click the icon to view the data.

a.Determine the hypotheses for the test. Choose the correct answer below.

A.H0:10 H1:1<0

C.H0:10 H1:1>0

Find the test statistic.tSTAT=

What is the p-value? p-value = Reach a decision.

(1) size of the apartment and the monthly rent.

b.The 95% confidence interval is (Round to four decimal places as needed.)

3: Size and Rent Data

B.H0:1=0 H1:10

D.H0:0=0 H1:00

(Round to two decimal places as needed.)

(Round to three decimal places as needed.)

H0. There is (2)

evidence to conclude that there is a linear relationship between the 1.

Size (square feet)

Rent ($)

1,925 2,575 2,200 2,525 1,975 2,725 2,625 1,935 1,875 2,150 2,425 2,650 3,275 2,800 2,375 2,450 2,100 2,725 2,175 2,150 2,575 2,650 2,175 1,800 2,750

850 1,460 1,095 1,232 708 1,495 1,126 716 690 946 1,090 1,295 1,985 1,369 1,185 1,215 1,255 1,249 1,150 906 1,371 1,030 745 1,010 1,210

(1)Do not reject(2)Reject

sufficient insufficient