Reference no: EM132318298

1: A sample of 61 observations is selected from one population with a population standard deviation of 0.65. The sample mean is 2.65. A sample of 48 observations is selected from a second population with a population standard deviation of 0.61. The sample mean is 2.52. Conduct the following test of hypothesis using the 0.01 significance level:

H₀: μ₁ - μ₂ ≤ 0

H₁: μ₁ - μ₂ > 0

a. Is this a one-tailed or a two-tailed test?

This is a one-tailed test.

b. State the decision rule. (Round the final answer to 2 decimal places.)

The decision rule is to reject H₀ if z is greater than ______________.

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

The test statistic is z  __________________.

d. What is your decision regarding H₀?

H₀ is not rejected

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

The p-value is______________.

2: A financial services company has 34 female top executives (presidents or vice presidents) among its 393 senior managers in its Banking Services division, while only 15 female top executives among its 315 senior managers in its Investment Services division. Test at the 0.05 significance level if this reveals the Banking Services division has significantly more female top executives in higher levels of management.

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

If z  is more than__________, reject H₀.

b. Compute the pooled proportion. (Round the final answer to 5 decimal places.)

p_c =________________.

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

The test statistic is_____________.

d. What is your decision regarding the null hypothesis?

Reject H₀. The Banking Services division has significantly more female top executives.

3:A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 38 subscribers to Plan A is $55,600 with a standard deviation of $8,300. This distribution is positively skewed; the coefficient of skewness is not larger. For a sample of 45 subscribers to Plan B, the mean income is $56,100 with a standard deviation of $8,000.

At the 0.02 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger?

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

Reject H₀ if t >__________.

b. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.)

Value of the test statistic  ________________.

c. What is your decision regarding the null hypothesis?

Do not reject  H₀. There is not enough evidence to conclude that the mean income of those selecting Plan B is not larger.

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

4: Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism, which 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 2 1

2 3 5

3 6 3

4 5 2

5 3 4

6 1 3

7 1 1

8 3 3

At the .05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.

a. State the decision rule for 0.05 significance level: H₀ : μ_d ≤ 0; H₁ : μ_d > 0. (Round the final answer to 3 decimal places.)

Reject H₀ if t > _______________.

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

Value of the test statistic _______________-      

c. Estimate the p-value? (Round the final answer to 4 decimal places.) _____________________.

d. What is your decision regarding H₀?

At the 0.05 significance level, do not reject.

5: Given the following sample information, test the hypothesis that the treatment means are equal at the 0.02 significance level:

Treatment 1 Treatment 2 Treatment 3

3 9 6

2 6 3

5 5 5

1 6 5

3 8 5

1 5 4 

4 1 

7 5 

6  

4

a. State the null hypothesis and the alternative hypothesis.

H₀: μ₁   = μ₂     =μ₃

H₁: Treatment means are not all the same.

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

Reject H₀ if F >   ____________.

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

SST =

SSE =

SS total =

d. Complete the ANOVA table. (Round the SS, MS, and F values to 2 decimal places.)

Source SS DF MS F    

Factor

Error

Total

e. State your decision regarding the null hypothesis.

Decision: Reject H0.

f. Find the 95% confidence interval for the difference between treatment 2 and 3. (Round the final answers to 2 decimal places.)

95% confidence interval is: ___________ ± ______________.

We can conclude that the treatments 2 and 3 are different.

6: The following hypotheses are given:

H₀ : σ₁² - σ₂² ≤ 0

H₁ : σ₁² - σ₂² > 0

A random sample of seven observations from the first population resulted in a standard deviation of 26. A random sample of thirty one observations from the second population showed a standard deviation of 21. At the 0.01 significance level, is there more variation in the first population?

a. State the decision rule. (Round the final answer to 2 decimal places.)

Reject H₀ if F >    ________________.

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

Value of the test statistic   ________________.

c. What is your decision regarding H_o?  Do not reject.

7:The null and alternative hypotheses are:

H0:μd≤0

H1:μd>0

The following sample information shows the number of defective units produced on the day shift and the afternoon shift for a sample of four days last month.

Day   Day Day  Day

1 2 3 4 

Day shift 11 12 12 18  

Afternoon shift 9 10 11 16

At the 0.01 significance level, can we conclude there are more defects produced on the Afternoon shift?

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

H₀ is rejected if t > _____________.

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

Test statistic_______________.

c. What is your decision regarding the null hypothesis?

H₀ should be rejected.

d. Determine the p-value. (Round the final answer to 4 decimal places.)

The p-value is______________.