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# Hypothesis Testing of Mean

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System data for a job shop revealed that the average time spent by a job in the shop was approximately n = 5 working days. A random sample of size five is taken with time spent in the shop, 3.7, 4.6, 3.9, 4.1, and 3.8. Is the output consistent with system behavior? (Why?). Construct a statistical test using a level of significance of alpha = 0.05

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Statistical testing using a level of significance
System data for a job shop revealed that the average time spent by a job in the shop was approximately n = 5 working days. A random sample of size five is taken with time spent in the shop, 3.7, 4.6, 3.9, 4.1, and 3.8. Is the output consistent with system behaviour? (Why?). Construct a statistical test using a level of significance of alpha = 0.05
The null hypothesis tested is
H0: Average time spent by the job in the shop = 5 working days (µ = 5)
The alternative hypothesis is
H1: Average time spent by the job in the shop ≠ 5 working days (µ ≠ 5)
Significance level = 0.05
Test Statistic used is . Given that = 4.02, n = 5, s = 0.356370594 (Please see the excel sheet)
Therefore, = -6.14906689
Decision rule: Reject the null hypothesis, if the absolute value of calculated test statistic is greater than the critical value of t with 4 d.f. at the significance level 0.05.
Lower critical value = -2.776445105
Upper critical value = 2.776445105
Conclusion: Reject the null hypothesis, since the absolute value of calculated test statistic is greater than the critical value. The sample provides enough evidence to conclude that average time spent by a job in the shop is different from 5 working days. Hence the output is not consistent with system behaviour.
Details
t Test for Hypothesis of the Mean

Data
Null Hypothesis = 5
Level of Significance 0.05
Sample Size 5
Sample Mean 4.02
Sample Standard Deviation 0.356370594

Intermediate Calculations
Standard Error of the Mean 0.159373775
Degrees of Freedom 4
t Test Statistic -6.14906689

Two-Tail Test
Lower Critical Value -2.776445105
Upper Critical Value 2.776445105
p-Value 0.003547921
Reject the null hypothesis

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