10) Do government employees take longer coffee breaks than private he That is a
ID: 3351611 • Letter: 1
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10) Do government employees take longer coffee breaks than private he That is a question that interested a management consultant a random sample of ten government employees and another sector workers To examine the issue, he took random sample of ten private coffee breaks and measured the amount of time (in minutes) they spent in during the day. The results are listed below Government EmployeesPrivate-Sector Workers 23 18 34 31 28 25 19 18 25 27 32 21 28 25 21 21 20 16 T6) a) Test an appropriate hypotheses to verify whether or not the variances of the two populations are equal. Use alpha-0.05Explanation / Answer
a)
Test and CI for Two Variances: govt., private
Method
Null hypothesis (govt.) / (private) = 1
Alternative hypothesis (govt.) / (private) 1
Significance level = 0.05
F method was used. This method is accurate for normal data only.
Statistics
95% CI for
Variable N StDev Variance StDevs
govt. 10 5.412 29.289 (3.723, 9.880)
private 10 3.629 13.167 (2.496, 6.624)
Ratio of standard deviations = 1.491
Ratio of variances = 2.224
95% Confidence Intervals
CI for
CI for StDev Variance
Method Ratio Ratio
F (0.743, 2.993) (0.553, 8.956)
Tests
Test
Method DF1 DF2 Statistic P-Value
F 9 9 2.22 0.249
p-value > 0.05
we fail to reject the null hypothesis
b)
Two-Sample T-Test and CI: govt., private
Two-sample T for govt. vs private
N Mean StDev SE Mean
govt. 10 27.20 5.41 1.7
private 10 21.50 3.63 1.1
Difference = (govt.) - (private)
Estimate for difference: 5.70
95% CI for difference: (1.37, 10.03)
T-Test of difference = 0 (vs ): T-Value = 2.77 P-Value = 0.013 DF = 18
Both use Pooled StDev = 4.6074
p-value = 0.013 < 0.05
we reject the null hypothesis ,the data provide sufficient evidence
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