Question

The mean consumption of water per household in a city was 1210 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 94 households was found to be 1167 cubic feet per month. The population standard deviation is given to be 223 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?

p-value =

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.

Round your answer to four decimal places.

Answer 1

a) Test statistic z =

                            

                              = -1.87

P-value = P(Z < -1.87)

             = 0.0307

Since P-value > = 0.01, we cannot not reject the null hypothesis.

b) For = 0.01 the critical value z^* = -2.33

Since the test statistic z is not less than the critical value z^*, we cannot reject the null hypothesis.