Question

A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properly, a random sample of 50 bottles was selected and the mean number of ounces for the 50 bottles was computed. A test of the hypotheses H0 : μ = 12 versus HA : μ < 12 was conducted, where μ represents the population mean number of ounces of the beverage dispensed by the machine. The p-value for the test was 0.08. Which of the following is the most appropriate conclusion to draw at the significance level of α = 0.05 ?
a. Because the p-value is greater than the significance level, there is not convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.
b. Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.
c. Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.
d. Because the p-value is less than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

Answer 1

Answer:

Option c) Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 12 ounces

Sample size, n = 50

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 12\\H_A: \mu < 12$

We use one-tailed  test to perform this hypothesis.

P-value = 0.08

Since the p value is greater than the significance level, we fail to reject the null hypothesis and accept it.

Thus, the machine is working properly and dispense 12 ounces of a beverage into a bottle.

Option c) Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.