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

Answer 1

Solution :

= 2

= 1.97

s = 0.1

n = 16

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

= -1.2

P (Z < -1.2 ) = 0.1151

P-value = 0.1151

= 0.05  

0.1151 > 0.05

Fail to reject the null hypothesis .

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