Understanding Hypothesis Testing

Jude tests if the automated machine at his restaurant fills drinks with the correct amount. He uses a sample of 20 drinks to test the null hypothesis that the population mean is 530 milliliters against the alternative that it is not. The sample mean is 528 milliliters with a standard deviation of 4 milliliters, resulting in a t-statistic of -2.236 and a p-value of 0.038. Since the p-value is less than the significance level of 0.05, the null hypothesis is rejected, suggesting the true mean is different from 530 milliliters.

What is the null hypothesis in Jude's experiment?

• The mean filling amount is 528 milliliters.

• The mean filling amount is 530 milliliters.

• The mean filling amount is not 530 milliliters.

• The mean filling amount is 532 milliliters.

What is the sample mean of the drinks in Jude's experiment?

• 530 milliliters

• 532 milliliters

• 528 milliliters

• 526 milliliters

What is the standard deviation of the sample in Jude's experiment?

• 6 milliliters

• 8 milliliters

• 4 milliliters

• 2 milliliters

What does a p-value represent in hypothesis testing?

• The probability of the sample mean being equal to the population mean.

• The probability of the null hypothesis being true.

• The probability of obtaining a result at least as extreme as the observed one, assuming the null hypothesis is true.

• The probability of the alternative hypothesis being true.

What is the significance level used in Jude's experiment?

• 0.20

• 0.05

• 0.01

• 0.10

What conclusion is drawn if the p-value is less than the significance level?

• Accept the alternative hypothesis.

• Reject the null hypothesis.

• Accept the null hypothesis.

• Fail to reject the null hypothesis.

What does rejecting the null hypothesis suggest in Jude's experiment?

• The mean filling amount is more than 530 milliliters.

• The mean filling amount is less than 530 milliliters.

• The mean filling amount is exactly 530 milliliters.

• The mean filling amount is different from 530 milliliters.

Which choice correctly reflects the conclusion of Jude's experiment?

• Accept the null hypothesis.

• Fail to reject the null hypothesis.

• Reject the null hypothesis; strong evidence suggests the mean is different from 530 milliliters.

• There is not enough evidence to make a conclusion.

What is the p-value obtained in Jude's experiment?

• 0.068

• 0.038

• 0.048

• 0.058

Why is the null hypothesis rejected in Jude's experiment?

• Because the sample size is too small.

• Because the p-value is less than the significance level.

• Because the p-value is greater than the significance level.

• Because the sample mean is exactly 530 milliliters.