Question

a company claims that the mean monthly residential electricity consumption in a certain region is more than 880 kilowatt-hours (kwh). you want to test this claim. you find that a random sample of 70 residential customers has a mean monthly consumption of 910 kwh. assume the population standard deviation is 124 kwh. at α = 0.05, can you support the claim? complete parts (a) through (e).

(c) find the standardized test statistic. use technology.
the standardized test statistic is z = 2.02.
(round to two decimal places as needed.)

(d) decide whether to reject or fail to reject the null hypothesis.
a. reject ( h_0 ) because the standardized test statistic is in the rejection region.
b. fail to reject ( h_0 ) because the standardized test statistic is not in the rejection region.
c. reject ( h_0 ) because the standardized test statistic is not in the rejection region.
d. fail to reject ( h_0 ) because the standardized test statistic is in the rejection region.

(e) interpret the decision in the context of the original claim.
at the 5% significance level, there enough evidence to the claim that the mean monthly residential electricity consumption in a certain region kwh.

Explanation:

Step1: <Understand the Hypothesis Test>

We are conducting a one - tailed z - test. The null hypothesis \(H_0:\mu\leq880\) and the alternative hypothesis \(H_1:\mu > 880\) (the company's claim). The significance level \(\alpha = 0.05\). For a right - tailed test, the critical value \(z_{\alpha}\) is \(z_{0.05}=1.645\) (using standard normal distribution tables or technology). The rejection region is \(z>1.645\).

Step2: <Analyze the Test Statistic and Rejection Region>

We are given the standardized test statistic \(z = 2.02\). Since \(2.02>1.645\) (the test statistic falls in the rejection region), we reject the null hypothesis \(H_0\).

Step3: <Interpret the Decision>

When we reject \(H_0\), we support the alternative hypothesis.

Answer:

At the \(5\%\) significance level, there is enough evidence to support the claim that the mean monthly residential electricity consumption in a certain region is more than \(880\) kWh.