Question

The security department of a campus wants to know whether the true average time required by a guard to walk his round is 30 minutes. A random sample of 36 rounds yielded the sample mean time 31.2 with the sample variance 9. Assume that the population is normal, and then: (a) Given 0.02 level of significance, determine whether this is a sufficient evidence to conclude that the true average time is not 30 minutes. (b) Find a corresponding p-value and give examples of α when the null hypothesis is rejected and not rejected, respectively.

Answer 1

Solution :

= 30

=31.2

S2 = 9

S = 3

n = 36

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 30

Ha :     30

Test statistic = t

= ( - ) / S / n

= (31.2 - 30 ) / 3 / 36

= 2.4

Test statistic = t = 2.4

P-value =0.0220

= 0.02  

P-value >

0.0220 > 0.02

Do not reject the null hypothesis .

There is insufficient evidence to suggest that