A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, how large could the sample mean be before they would reject the null hypothesis?
A) 16.2 ounces
B) 16.049 ounces
C) 15.8 ounces
D) 16.041 ounces

Question

Quizplus · Accepted Answer

The critical value for a two-tailed test at a 0.10 significance level is approximately 1.645. Using the formula for the z-test: z = (X̄ - μ) / (σ/√n), where X̄ is the sample mean, μ is the population mean (16 ounces), σ is the standard deviation (0.20 ounces), and n is the sample size (64), we solve for X̄. The sample mean should not exceed 16.041 ounces to not reject the null hypothesis.

A Company That Makes Shampoo Wants to Test Whether the Average