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
FTest TwoSample 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) onetail 
0.124675612 

F Critical onetail 
3.178893104 
tTest: TwoSample 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) onetail 
? 

t Critical onetail 
? 

P(T<=t) twotail 
? 

t Critical twotail 
? 
tTest: TwoSample 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) onetail 
? 

t Critical onetail 
? 

P(T<=t) twotail 
? 

t Critical twotail 
? 
tTest: 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) onetail 
? 

t Critical onetail 
? 

P(T<=t) twotail 
? 

t Critical twotail 
? 
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
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  pvalue (onetailed, upper) 
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