Question

The mean consumption of water per household in a city was 1238 cubic feet per month. Due to a water shortage because of a drought, the city council campaigned for water use conservation by households. A few months after the campaign was started, the mean consumption of water for a sample of 96 households was found to be 1153 cubic feet per month. The population standard deviation is given to be 261 cubic feet.

a. Find the p-value for the hypothesis test that the mean consumption of water per household has decreased due to the campaign by the city council. Would you reject the null hypothesis at α=0.01?

b. Make the test of part a using the critical-value approach and α=0.01.

Round your answer for z to two decimal places.

Answer 1

Solution :

=  1238

=1153

=261

n = 96

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    =  1238

Ha :      1238

Test statistic = z

= ( - ) / / n

= (1153 - 1238) / 261 / 96

= -3.19

Test statistic = z = -3.19

P(z < -3.19 ) =  0.0007

P-value = 2*0.0007 =0.0014

= 0.05  

P-value <

0.0014 < 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that