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

This is the two tailed test .

The null and alternative hypothesis is

H₀ : = 30

H_a : 30

Test statistic = t

= ( - ) / s / n

= (30.9 - 30) / 1.8 / 45

Test statistic = 3.354

df = 44

P-value = 0.0016

= 005

P-value <

Reject the null hypothesis .

There is

There is sufficient evidence to conclude that the null hypothesis μ=30 minutes in favor of the alternative hypothesis μ≠30 minutes.