Question

Please use the p-value approach to conduct a hypothesis test for the following problem. Please provide detailed solutions in the four steps to hypothesis testing.

The security department of a factory wants to know whether the true average time required by the night guard to walk his round is 30 minutes. If, in a random sample of 45 rounds, the night guard averaged 30.9 minutes with a standard deviation of 1.8 minutes, determine whether this is sufficient evidence to reject the null hypothesis μ=30 minutes in favor of the alternative hypothesis μ≠30 minutes. Use the 0.05 level of significance.

Answer 1

H0: = 30, Ha: 30

This is two tailed test,

Test statistics

t = ( - ) / ( S / sqrt(n) )

= (30.9 - 30) / ( 1.8 / sqrt(45) )

= 3.35

df = n - 1 = 45 - 1 = 44

From T table,

With test statistics 3.35 and df of 44,

p-value (two tailed) = 0.0017

Since p-value < 0.05 level ,

Reject the null hypothesis