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. To test DullCo's hypothesis, the test statistic is:
A)-1.980
B)-1.728
C)-2.101
D)-1.960

Question

Quizplus · Accepted Answer

The test statistic for this hypothesis test is calculated using the formula for a t-test because the population standard deviation is unknown and the sample size is small (n < 30). The formula is: $ t = \frac{\bar{x} - \mu}{(s/\sqrt{n})} $, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values: $ t = \frac{37.8 - 40}{(5.4/\sqrt{18})} = -1.728 $.

Dullco Manufacturing Claims That Its Alkaline Batteries Last at Least