Question

A house cleaning service claims that it can clean a four bedroom house in less than 2 hours. A sample of n = 16 houses is taken and the sample mean is found to be 1.97 hours and the sample standard deviation is found to be 0.1 hours. Using a 0.05 level of significance what is the correct conclusion?

There is not enough evidence to conclude that the mean time is less than 2 hours.

There is enough evidence to conclude that the mean time is more than 2 hours.

There is not enough evidence to conclude that the mean time is greater than 2 hours.

There is enough evidence to conclude that the mean time is less than 2 hours.

Answer 1

Solution :

This is the left tailed test,  

The null and alternative hypothesis is ,

H0 :   = 2

Ha : < 2

Test statistic = t =

= ( - ) / s / n

= (1.97 - 2) / 0.1 / 16

Test statistic = t = -1.20

degrees of frredom = n - 1 = 16 - 1 = 15

P(t < -1.20)

P-value = 0.1244

= 0.05  

P-value >

Fail to reject the null hypothesis .

There is not enough evidence to conclude that the mean time is less than 2 hours.