Question

Use the following to answer the next question. 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	?

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

a) H0: µ(government) - µ(private) = 0, Ha: µ(government) - µ(private) < 0

b)H0: µ(government) - µ(private) = 0, Ha: µ(government) - µ(private) > 0

c)H0: µ(government) - µ(private) = 0, Ha: µ(government) - µ(private) ≠ 0

d)H0: µ(government) - µ(private) ≠ 0, Ha: µ(government) - µ(private) = 0

Answer 1

b)H0: µ(government) - µ(private) = 0, Ha: µ(government) - µ(private) > 0

1	2
27.2	21.5	mean
5.411931263	3.628636107	std. dev.
10	10	n
	18	df
	5.7000	difference (1 - 2)
	21.2280	pooled variance
	4.6074	pooled std. dev.
	2.0605	standard error of difference
	0	hypothesized difference
	2.766	t
	.0064	p-value (one-tailed, upper)

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