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.

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

[tex]H_{0}: \mu = 12\\H_A: \mu < 12[/tex]

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.

astha8579 astha8579 · Answer 2 · 2022-01-13T10:59:52+01:00

Since the p-value found is more than the level of significance, thus in such case, we can't reject the null hypothesis, and thus accept it.

Thus:

"Option C): 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.

Given that:

Proposed mean of population = [tex]\mu_0 = 12[/tex]

Real population mean (unknown parameter) = [tex]\mu[/tex]

Size of sample = [tex]n = 50[/tex]

Null Hypothesis = [tex]H_0 : \mu = 12 = \mu_0[/tex]

Alternate Hypothesis = [tex]H_A: \mu < 12 = \mu_0[/tex]

p-value found = 0.08

Level of significance = [tex]\alpha = 0.05[/tex]

How to form the hypotheses and test them?

Since the p-value found is more than the level of significance, thus in such case, we can't reject the null hypothesis, and thus accept it.

Null hypothesis is the favored hypothesis which we test. The test's result just tells whether the null hypothesis is acceptable or not. The alternative hypothesis is accepted when the null hypothesis is rejected, else we accept the null hypothesis.

Thus, [tex]H_0 : \mu = 12 = \mu_0[/tex] is accepted as [tex]\text{p-value} = 0.08 > 0.05 = \alpha[/tex] and we deduce that:

"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."

is correct option.

Learn more about null hypothesis and alternative hypothesis here:

https://brainly.com/question/10758924