# MATHEMATICS

1.

Ms. Lisa Monnin is the budget director for Nexus Media Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.

Sales ($) 127 137 140 159 136 138

Audit ($) 122 103 127 136 149 120 142

At the 0.01 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff?

(a) State the decision rule. (Round your answer to 3 decimal places.)

Reject H0 if t >

(b) Compute the pooled estimate of the population variance. (Round your answer to 2 decimal places.)

Pooled variance

(c) Compute the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic

2

Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. Assume the population standard deviations are not the same. The following is the amount ($000) earned per month by a sample of Claiborne models:

$5 $4.5 $3.4 $3.4 $6 $3.3 $4.5 $4.6 $3.5 $5.2

4.8 4.4 4.6 3.6 5

The following is the amount ($000) earned by a sample of Klein models.

$3.1 $3.7 $3.6 $4 $3.8 $3.8 $5.9 $4.9 $3.6 $3.6

2.3 4

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

Degrees of freedom

(2) State the decision rule for 0.05 significance level: H0: μLC ≤ μCK; H1: μLC > μCK. (Round your answer to 3 decimal places.)

Reject H0 if t>

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

Value of the test statistic

3A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below.

Statistic Men Women

Sample mean 25.24 21.73

Population standard deviation 5.53 4.54

Sample size 34 37

________________________________________

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 your decision regarding on null hypothesis?

The decision is the null hypothesis that the means are the same.

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

p-value

Suppose the manufacturer of Advil, a common headache remedy, recently developed a new formulation of the drug that is claimed to be more effective. To evaluate the new drug, a sample of 270 current users is asked to try it. After a one-month trial, 251 indicated the new drug was more effective in relieving a headache. At the same time a sample of 390 current Advil users is given the current drug but told it is the new formulation. From this group, 352 said it was an improvement.

(1) State the decision rule for .01 significance level: H0: πn ≤ πc; H1: πn > πc. (Round your answer to 2 decimal places.)

Reject H0 if z >

(2) Compute the value of the test statistic. (Do not round the intermediate value. Round your answer to 2 decimal places.)

Value of the test statistic

5Lester 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. 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 What is the critical F value for a sample of four observations in the numerator and seven in the denominator? Use a one-tailed test and the .01 significance level. (Round your answer to 2 decimal places

8 The following hypotheses are given.

Ho : σ1² = σ2²

H1 : σ1² ≠ σ2²

A random sample of eight observations from the first population resulted in a standard deviation of 10. A random sample of six observations from the second population resulted in a standard deviation of 7.

(1) State the decision rule for .02 significance level: (Round your answer to 1 decimal place.)

Reject Ho if F >

(2) Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Value of the test statistic

9A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.

Clothes Food Toys

26 45 60

21 48 51

43 43 43

35 53 54

28 47 63

31 42 53

17 34 48

31 43 58

20 57 47

47 51

44 51

54

________________________________________

(1) Complete the ANOVA table. Use .05 significance level. (Round the SS and MS values to 1 decimal place and F value to 2 decimal places. Leave no cells blank – be certain to enter “0” wherever required. Round the DF values to nearest whole number.)

Source DF SS MS F P

Factors

Error

________________________________________ ________________________________________

Total

________________________________________________________________________________ ________________________________________________________________________________

________________________________________

(2) Find the values of mean and standard deviation. (Round the mean and standard deviation values to 3 decimal places.)

Level N Mean StDev

Clothes

Food

Toys

________________________________________

12,13,14

Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.

Treatment 1 Treatment 2 Treatment 3

8 3 3

11 2 4

10 1 5

3 4

2

________________________________________

12 (b) What is the decision rule? (Round your answer to 2 decimal places.)

Reject Ho if F >

13(c) Compute SST, SSE, and SS total. (Round your answers to 2 decimal places.)

SST

SSE

________________________________________

SS total

14(d) Complete an ANOVA table. (Round F, SS to 2 decimal places and MS to 3 decimal places.)

Source SS df MS F

Treatments

Error