Business Statistics Homework Assignment ESSAY

Business Statistics Homework Assignment

1) The null and alternate hypotheses are:

H0 : μ1 = μ2

H1 : μ1 ≠ μ2

A random sample of 8 observations from one population revealed a sample mean of 23 and a sample standard deviation of 3.9. A random sample of 8 observations from another population revealed a sample mean of 28 and a sample standard deviation of 4.4.

At the 0.05 significance level, is there a difference between the population means?

a. State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)

The decision rule is to reject H0 if t < _________ or t > __________ .

b. Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.)

Pooled estimate of the population variance = ____________

c. Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Test statistic = ______________

2) Businesses, particularly those in the food preparation industry such as General Mills, Kellogg, and Betty Crocker regularly use coupons as a brand allegiance builder to stimulate their retailing. There is uneasiness that the users of paper coupons are different from the users of e-coupons (coupons disseminated by means of the Internet). One survey recorded the age of each person who redeemed a coupon along with the type (either electronic or paper). The sample of 27 e-coupon users had a mean age of 32.2 years with a standard deviation of 9.0, while a similar sample of 21 traditional paper-coupon clippers had a mean age of 38.2 with a standard deviation of 5.7.

a) Find the degrees of freedom for unequal variance test. (Round down answer to nearest whole number.)

Degrees of freedom ___________

b) State the decision rule for 0.10 significance level: H0: μe = μp; H1: μe ≠ μp. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)

Reject H0 if t <________ or t > __________

c) Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Value of the test statistic ___________

3) A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. Assume the population standard deviation for those drinking regular coffee is 1.31 cups per day and 1.42 cups per day for those drinking decaffeinated coffee. A random sample of 52 regular-coffee drinkers showed a mean of 4.35 cups per day. A sample of 48 decaffeinated-coffee drinkers showed a mean of 5.69 cups per day.

Use the .05 significance level.

a) The decision rule is to reject H0: μr ≥ μd if z <____________ . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) b) The test statistic is z =____________ . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) c) The p-value is ____________. 4) A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary. The sample information is submitted to MINITAB with the following results: Analysis of Variance Source df SS MS F Factor 3 32.27 10.76 13.90 Error 10 7.74 .77 Total 13 40.01 Reject H0 if F >___________ . (Round your answer to 2 decimal places.)

5)

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are not equal. The information is summarized below.

Statistic Men Women

Sample mean 25.17 22.50

Sample standard deviation 5.69 4.51

Sample size 34 36

At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?

a) Compute the value of the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic ___________

b) What is the p-value? ____________ (Round your answer to 4 decimal places.)

p-value

6) Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months following the exercise program. Below are the results.

Employee Before After

1 6 3

2 6 2

3 7 1

4 7 2

5 4 2

6 6 6

7 6 3

8 6 7

At the 0.10 significance level, can he conclude that the number of absences has declined? Hint: For the calculations, assume the “Before” data as the first sample.

Reject H0 if t >____________ . (Round your answer to 3 decimal places.)

The test statistic is_______________ . (Round your answer to 3 decimal places.)

7) Arbitron Media Research Inc. conducted a study of the iPod listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for men was 32 minutes per day. The standard deviation of the sample of the 10 men studied was 13 minutes per day. The mean listening time for the 11 women studied was also 32 minutes, but the standard deviation of the sample was 13 minutes. At the .10 significance level, can we conclude that there is a difference in the variation in the listening times for men and women? (Round your answer to 3 decimal places.)

The test statistic is ____________

8)

Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order to test different advertising approaches, it uses different media to reach potential buyers. The mean annual family income for 18 people making inquiries at the first development is $162,000, with a standard deviation of $40,000. A corresponding sample of 29 people at the second development had a mean of $181,000, with a standard deviation of $29,000. Assume the population standard deviations are the same.

1.

State the decision rule for .01 significance level: H0: μ1 = μ2; H1:μ1 ≠ μ2. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Reject H0 if t is not between__________ and ___________.

2.

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Value of the test statistic__________

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