A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properl

Question

20 days ago

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A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properl

y, 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.

Mathematics

1 answer:

zzz [9K] · Answer 1 · 2026-03-08T08:42:30+03:00

Answer:

Option c) The population mean amount of ounces dispensed into a bottle is 12 ounces, as indicated by the p-value exceeding the threshold for significance.

Step-by-step explanation:

In the question, we are provided with the following:

Mean of the population, μ = 12 ounces

Sample size, n = 50

Alpha, α = 0.05

Initially, we formulate the null and alternative hypotheses:

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

The one-tailed test is utilized for this hypothesis test.

P-value = 0.08

Given that the p-value is beyond the significance level, we do not reject the null hypothesis, thus accepting it.

This implies that the machine operates correctly and dispenses 12 ounces of liquid into each bottle.

Option c) The evidence suggests that the mean quantity dispensed per bottle is indeed 12 ounces since the p-value is over the significance level.

A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properl

Ensure that one of them is a match.