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 mu = 30 minutes in favor of the alternative hypothesis mu does not equal 30 minutes. Use the 0.05 level of significance.

Answer 1

Solution :

= 30

=30.9

S =1.8

n = 45

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 30

Ha :     30

Test statistic = t

= ( - ) / S / n

= (30.9 -30 ) / 1.8 / 45

= 3.354

Test statistic = t =3.354  

P-value =0.9983

= 0.05  

P-value >

0.9983 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that