# Hypothesis Testing of Mean

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

Answer

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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