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

Solution :

Given that,

Population mean = = 30

Sample mean = = 30.9

Sample standard deviation = s = 1.8

Sample size = n = 45

Level of significance = = 0.05

Step - 1

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 30

Ha: 30

Step - 2

The test statistics,

t = ( - )/ (s/)

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

= 3.354

Step - 3

P-value = 0.0016

The p-value is p = 0.0016 < 0.05, it is concluded that the null hypothesis is rejected.

Step - 4

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that true average time required by the night guard to walk his round is 30 minutes, at the 0.05 significance level.