In a bottling process,a manufacturer will lose money if the bottles contain either more or less than is claimed on the label.Suppose a quality manager for a steak sauce company is interested in testing whether the mean number of ounces of steak sauce per restaurant size bottle differs from the labeled amount of 20 ounces.The manager samples nine bottles,measures the weight of their contents,and finds the sample mean is 19.7 ounces and the sample standard deviation is 0.3 ounces.Calculate the appropriate test statistic to test the hypotheses.
A)3.00
B)1.00
C)-9.00
D)-1.00
E)-3.00

Question

Quizplus · Accepted Answer

The appropriate test statistic to test the hypotheses is a t-test, since the population standard deviation is unknown and the sample size is less than 30. We can use the formula:

t = (x̄ - μ) / (s / √n)

where x̄ is the sample mean, μ is the hypothesized population mean (20 ounces), s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (19.7 - 20) / (0.3 / √9)
t = -0.3 / 0.1
t = -3.00

Therefore, the appropriate test statistic is -3.00, which corresponds to choice E. This means that the sample mean is 3 standard errors below the hypothesized population mean of 20 ounces.

In a Bottling Process,a Manufacturer Will Lose Money If the Bottles