A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual mean amount is less.The consumer obtained a sample of 49 cups of the dispensed liquid with average of 7.75 ounces.If the sample variance of the dispensed liquid delivered per cup is 0.81 ounces, and α = 0.05, the appropriate decision is to ________.
A)increase the sample size
B)reduce the sample size
C)fail to reject the 8-ounces claim
D)maintain status quo
E)reject the 8-ounces claim

Question

Quizplus · Accepted Answer

The hypothesis test here is aimed at determining if the mean amount of liquid dispensed is less than the claimed 8 ounces. Given the sample size (n=49), sample mean ($\bar{x}$ = 7.75 ounces), population variance ($\sigma^2$ = 0.81 ounces), and $\alpha = 0.05$, we can conduct a one-sample t-test (or z-test due to the sample size and variance being known). The calculated test statistic will show if the difference between the sample mean and the population mean (8 ounces) is statistically significant. Given the information, the decision to reject the null hypothesis (that the machine dispenses 8 ounces on average) is based on the sample mean being significantly less than the claimed mean, indicating the machine dispenses less than 8 ounces on average.

A Coffee-Dispensing Machine Is Supposed to Deliver 8 Ounces of Liquid