Question

The mean consumption of water per household in a city was 1218 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 1181 cubic feet per month. The population standard deviation is given to be 216 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=0.05?

Round your answer to four decimal places.

p-value =

b.Make the test of part a using the critical-value approach and α=0.05.

Round your answer for z to two decimal places.

z_observed =

Answer 1

Null Hypothesis, 1218

Alternative Hypothesis, 1218

xbar = 1181, n = 94
sigma = 216

test statistic,

z = (1181 -1218)/(216/sqrt(94))
z = -1.66

This is left tailed test,
p-value = P(z < -1.66)
p-value = 0.0485

b)

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

Reject H0 if test statistic, z < -1.64 (critical value)

z-observed = -1.66

Reject H0

There is sufficient evidence to conclude that mean consumption of water is decreased.