Q1. Do government employees take longer coffee breaks than private sector workers? That is a question that interested a management consultant. To examine the issue, he took a random sample of ten government employees and another random sample of ten private sector workers and measured the amount of time (in minutes) they spent in coffee breaks during the day (the samples are assumed to be independent).

PS: Relevant outputs are given below; please refer to them in order to answer the following questions.

Variable 1: Government Employees

Variable 2: Private Sector Employees

F-Test Two-Sample for Variances:

Variable 1 Variable 2

Mean: 27.2 21.5

Variance: 29.28888889 13.16666667

Observations: 10 10

df: 9 9

F: 2.224472574

P(F<=f) one-tail: 0.124675612

F Critical one-tail: 3.178893104

t-Test: Two-Sample Assuming Equal Variances:

Variable 1 Variable 2

Mean: 27.2 21.5

Variance: 29.28888889 13.16666667

Observations: 10 10

Pooled Variance: 21.22777778

Hypothesized Mean Difference: 0

df: ?

t Stat: ?

P(T<=t) one-tail: ?

t Critical one-tail: ?

P(T<=t) two-tail: ?

t Critical two-tail: ?

t-Test: Two-Sample Assuming Unequal Variances:

Variable 1 Variable 2

Mean: 27.2 21.5

Variance: 29.28888889 13.16666667

Observations: 10 10

Hypothesized Mean Difference: 0

df: 16

t Stat: ?

P(T<=t) one-tail: ?

t Critical one-tail: ?

P(T<=t) two-tail: ?

t Critical two-tail: ?

t-Test: Paired Two Sample for Means

Variable 1 Variable 2

Mean: 27.2 21.5

Variance: 29.28888889 13.16666667

Observations: 10 10

Pearson Correlation: 0.226322699

Hypothesized Mean Difference: 0

df: ?

t Stat: 3.11

P(T<=t) one-tail: ?

t Critical one-tail: ?

P(T<=t) two-tail: ?

t Critical two-tail: ?

1.Do the data provide sufficient evidence at the 5% significance level to support the consultants claim? State the null and alternative hypotheses.

A. H0: (government) -(private) = 0, Ha: (government) -(private) < 0

B. H0: (government) -(private) = 0, Ha: (government) -(private) > 0

C. H0: (government) -(private) = 0, Ha: (government) -(private) 0

D. H0: (government) -(private) 0, Ha: (government) -(private) = 0

2.What type of test(s) are you using?

A. Only a paired samples t-test

B. Only an independent samples t-test

C. An F-test than a paired samples t-test

D. An F-test than an independent samples t-test

3.What is your test statistic?

A. 3.11

B. 2.22

C. 2.76

D. -2.76

4.What is the p-value?

A.0.006

B. 0.012

C. 0.12

D. 0.05

5.What is the critical value?

A. 2.1

B. 1.73

C. 3.17

D. 2.1

6.What is your conclusion?

A. Reject H0

B. Fail to reject H0

C. Reject Ha

D. Fail to reject Ha

7.What assumption(s) do you need to make in order to answer the above questions?

A.No assumptions are needed

B.The population distributions are assumed to be normal.

C. The population distributions are assumed to be t-distributed.

D. The sampling distribution of the sample means are assumed to be normal.