Question

The mean consumption of water per household in a city was 1212 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 92 households was found to be 1167 cubic feet per month. The population standard deviation is given to be 220 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?

Round your answer to four decimal places.

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.

z_observed =

We conclude that the mean consumption of water per household has Choose your answer; Conclusion

not decreaseddecreased

due to the campaign by the city council.

Answer 1

In this scenario our claim is that the mean consumption of water per household has decreased from 1212 due to the campaign by the city council. To test this hypothesis we have to use one sample z test because here the population standard deviations is known.

Based on sample information the test is performed at 0.01 level of significance as below,

The z critical value is calculated using Standerd normal z-table at 0.01 left tailed.

a) The p value is calculated as below,

P-value = 0.0249 .

The p value is calculated using Standerd normal z-table or using Excel you can calculate the p value.

b) using z critical value approch,

Z cal test Statistic = -1.96.

Since z cal = -1.96 > -2.33 hence we fail to rejecting Ho hypothesis.

Conclusion : Since p value is greater than alpha level of significance so we Fail to Reject Ho null hypothesis and it is concluded that the null hypothesis Ho is not rejected.

Therefore, there is not enough evidence to claim that the population mean μ is less than 1212, at the 0.01 significance level.

Yes the mean consumption of water per household has not decreased due to the campaign by the city council.

The result is not significant.

Thank you.