To evaluate the results of the hypothesis test using the provided data, we can follow these steps:
Step 1: State the null and alternative hypotheses.
- Null hypothesis (\(H_0\)): The population mean is equal to 120 volts (\(\mu = 120\)).
- Alternative hypothesis (\(H_1\)): The population mean is not equal to 120 volts (\(\mu \neq 120\)).
This is a two-tailed test.
Step 2: Determine the critical value(s) for a significance level of 0.05. For a two-tailed test with a significance level of 0.05, we split the alpha into two tails, so each tail has an alpha of 0.025.
Using a Z-distribution table, the critical Z-values corresponding to the 0.025 in each tail are approximately \(-1.96\) and \(1.96\).
Step 3: Compare the test statistic to the critical value. The test statistic calculated is 73.242, which is far greater than 1.96.
Step 4: Make a decision. Since the test statistic (73.242) falls outside the range defined by the critical values (-1.96, 1.96), we reject the null hypothesis.
Step 5: State the conclusion. Since we rejected the null hypothesis, we conclude that there is sufficient evidence to warrant a rejection of the claim that the mean voltage is 120 volts.
Thus, the final conclusion corresponds to:
B) Reject the null hypothesis; there is sufficient evidence to warrant a rejection of the claim that the mean voltage is 120 volts.