Answer to Question #194727 in Statistics and Probability for Alice

Question

In a particular community, it is claimed that the mean household water usage for a particular month is 45 cubic meters. The following year, a countrywide water conservation campaign was conducted. Forty nine homes were randomly selected and found that the mean consumption is 54 cubic meters with a standard deviation of 5 cubic meters. Is there enough evidence to say that the mean household water usage per month is higher than 45 cubic meters at a=0.01?

Answer 1

Null Hypothesis, $H_o:\mu>45$ , There is enough evidence to support the claim.

Alternative Hypothesis, $H_a: μ \le45$ ,There is no enough evidence to support the claim.

Test statistic,

$z= \dfrac{(\bar{x} - \mu)}{(\frac{\sigma}{\sqrt{n})}} \\[9pt] z = \dfrac{(45 - 54)}{(\frac{5}{\sqrt{49}}} \\[9pt] z = -12.6$

P-value Approach

P-value $=P(z>-12.6)=1$

As $P-value \ge 0.01$ , we Accept null hypothesis.

Hence , There is enough evidence to support the claim that the mean household water usage for a particular month is greater than 45 cubic meters.