A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 22 bottles and finds the average amount of liquid held by the bottles is 9.7 ounces with a standard deviation of .4 ounce. Calculate the appropriate test statistic.
A) $t = - 2.225$
B) $t = - 3.437$
C) $t = - 3.518$
D) $t = - 16.500$

Question

A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 22 bottles and finds the average amount of liquid held by the bottles is 9.7 ounces with a standard deviation of .4 ounce. Calculate the appropriate test statistic. 
A) $t = - 2.225$
B) $t = - 3.437$
C) $t = - 3.518$
D) $t = - 16.500$

Quizplus · Accepted Answer

The correct test statistic is t = -3.518. This is calculated by taking the difference between the sample mean and the hypothesized mean (10 ounces), and dividing by the standard error of the mean. The standard error of the mean is calculated by dividing the standard deviation by the square root of the sample size. In this case, the standard error of the mean is .4 / sqrt(22) = .0894. Therefore, the test statistic is (9.7 - 10) / .0894 = -3.518.

A Bottling Company Produces Bottles That Hold 10 Ounces of Liquid