Question

The mean consumption of water per household in a city was 1248 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 99 households was found to be 1181 cubic feet per month. The population standard deviation is given to be 221 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 Round your answer to four decimal places. p-value =Enter you answer; p-value We Choose you answer from the menu in accordance to the item a) of the question statement b. Make the test of part a using the critical-value approach and Round your answer for z to two decimal places. zobserved =Enter you answer; z_observed We Choose you answer from the menu in accordance to the item b) of the question statement We conclude that the mean consumption of water per household has Choose your answer; Conclusion due to the campaign by the city council.

Answer 1

Null Hypothesis, 1248

Alternative Hypothesis, 1248

xbar = 1181, sigma = 221, n = 99

test statistic,

z = (1181 - 1248)/(221/sqrt(99))
z = -3.02

this is left tailed test,
p-value = P(z < -3.02)
p-value = 0.0013

As p-value < 0.05, reject H0

Here the significance level, 0.05.

This is right tailed test; hence rejection region lies to the right. -1.64 i.e. P(z < -1.645) = 0.05

Reject H0 if test statistic, z < -1.64

Reject H0

There is significant evidence to conclude that the mean use of water is decreased due to campaign.