Final answer:
The test statistic does not exceed the critical value, thus we cannot reject the null hypothesis at the 0.01 significance level, indicating that there is insufficient evidence to support the manufacturer's claim.
Step-by-step explanation:
Hypothesis Testing for Battery Charges
To determine if there is enough evidence to support the manufacturer's claim that its rechargeable batteries are good for an average of more than 1000 charges, we conduct a hypothesis test at the 0.01 significance level.
a. State the hypotheses
The null hypothesis (H0): μ ≤ 1000 (The average number of charges is 1000 or fewer.)
The alternative hypothesis (H1): μ > 1000 (The average number of charges is greater than 1000.)
b. State the test statistic information
The test statistic is calculated using the formula for the z-score, which is (sample mean - population mean) / (standard deviation / sqrt(sample size)). Substituting the given values: (1002 - 1000) / (14 / sqrt(100)) = 2 / (14 / 10) = 1.43.
c. State either the p-value or the critical value
Since the significance level is 0.01, the corresponding critical z-value is approximately 2.33. But our test statistic is 1.43, which is less than the critical value.
d. State your conclusion and explain your reasoning
Because the test statistic does not exceed the critical value, we do not reject the null hypothesis. Therefore, there is not enough statistical evidence at the 0.01 significance level to support the manufacturer's claim that batteries are good for more than 1000 charges.