Question

A battery company produces typical consumer batteries and claims that their batteries last at least 100 hours, on average. Your experience with their batteries has been somewhat different, so you decide to conduct a test to see if the company’s claim is true. You believe that the mean life is actually less than the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample and obtain the following information: the sample mean is 98.5, the standard error of the mean is 0.777 and the number of observations is 20. What can you conclude:

Select one:

a. The mean life of batteries is typically less than 100 hours at the 1% level.

b. The mean life of batteries is typically less than 100 hours at the 5% level but not at the 2.5% level.

c. The mean life of batteries is typically more than 100 hours at the 5% level.

d. The mean life of batteries is typically more than 100 hours at the 10% level.

e. The mean life of batteries is typically less than 100 hours at the 2.5% level but not at the 1% level.

Answer 1

Solution:

The correct answer is:

b. The mean life of batteries is typically less than 100 hours at the 5% level but not at the 2.5% level.

Explanation:

The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

The p-value is:

The p-value is obtained the excel function:

Where:

-1.9305 is the test statistic

19 is the degrees of freedom

1 is the one-tailed test

Conclusion:

Since the p-value is less than the significance level 0.05 but greater than 0.025, we, therefore, can conclude that the mean life of batteries is typically less than 100 hours at the 5% level but not at the 2.5% level