Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. In a left-tailed test at α = .05, which is the most accurate statement?
A)We would strongly reject the claim.
B)We would clearly fail to reject the claim.
C)We would face a rather close decision.
D)We would switch to α = .01 for a more powerful test.

Question

Quizplus · Accepted Answer

To conduct a left-tailed test, the null hypothesis is that the true mean battery life is at least 40 hours, and the alternative hypothesis is that the true mean battery life is less than 40 hours. With a sample mean of 37.8 hours and a standard deviation of 5.4 hours, we can calculate the t-statistic as (37.8 - 40) / (5.4 / sqrt(18)) = -2.21. 
Using a t-distribution table with 17 degrees of freedom and a significance level of .05, the critical value is -1.740. Since our calculated t-statistic (-2.21) is less than the critical value (-1.740), we cannot reject the null hypothesis at the .05 level of significance. 
Therefore, the most accurate statement is that we would face a rather close decision.

Dullco Manufacturing Claims That Its Alkaline Batteries Last at Least