Mean Life Span of Batteries
A company sells portable walkie-talkie radios to construction crews. The batteries for these radios last for an average of 55 hours. The purchasing manager for this company receives a brochure in the mail that advertises a new brand of batteries. This new brand of batteries is cheaper than the brand that the company currently uses. However, the pricing manager is concerned that the cheaper batteries may have a shorter average battery life than the current brand. (Note: The number of hours that batteries last is called their battery life.) The pricing manager wants to perform a statistical test at the 1% level of significance to determine if the cheaper batteries have a shorter average battery life.
Step 1: Determine the Hypotheses
• State the null and alternative hypotheses for this test.
• Is this a left-tailed, right-tailed, or two-tailed test? Be sure to explain your answer.
Step 2: Collect the Data
To test this hypothesis, the pricing manager installs 40 randomly selected batteries of the new brand in the same walkie-talkie radios. He finds that the mean lifetime for the sample is 52 hours with a standard deviation of 10 hours.
• Does the manager's sample satisfy the criteria for the approximate normality of the sampling distribution of sample means? Be sure to explain your answer.
Step 3: Assess the Evidence
• Is the sample mean consistent with the alternative hypothesis?
• What is the test statistic for the observed sample mean?
• What is the P-value?
Step 4: State a Conclusion
• How does the P-value compare to the significance level? Should we reject or fail to reject the null hypothesis?
• What can you conclude about the alternative hypothesis?
• State a conclusion in the context of the problem.
• It is possible that the conclusion was incorrect. The new, cheaper batteries may indeed have a shorter lifespan than the old batteries. If this is the case, what type of error was made?