Question 1

Which of the following is the correct null hypothesis ($$H_0) $$for testing whether the mean age of pennies in circulation is 20 years old?

Accepted Answer

$$H_0$$: \mu = 20$$

Question 2

Given a sample mean $$\bar{x} = 21.15$$, sample standard deviation $$s = 12.43$$, and sample size $$n = 800$$, what is the value of the test statistic for testing $$H_0$$: \mu = 20$$?

Accepted Answer

$$t = \frac{21.15 - 20}{12.43/\sqrt{800}}$$

Question 3

Which condition must be satisfied to use the $$t-$$test for a population mean when $$\sigma is $$not known?

Accepted Answer

Both (a) and (b) must be satisfied.

Question 4

A researcher wants to test if the average time for a sand timer is different from 180 seconds. Which of the following is the correct alternative hypothesis ($$H_1$$)?

Accepted Answer

$$H_1$$: \mu 
eq 180$$

Question 5

If the p-value for a hypothesis test is 0.03 and $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 6

A sample of 50 quarters has a mean weight of 5.6218 g and a standard deviation of 0.0682 g. Test the claim that the mean weight is less than 5.67 g. What is the correct form of the alternative hypothesis?

Accepted Answer

$$H_1$$: \mu \u003c 5.67$$

Question 7

Which formula is used to calculate the test statistic for a mean when the population standard deviation is not known?

Accepted Answer

$$t = \frac{\bar{x} - \mu}{s/\sqrt{n}}$$

Question 8

If a 95% confidence interval for the mean age of pennies is (20.29, 22.02), what can you conclude about the claim that the mean age is 20 years?

Accepted Answer

There is enough evidence to reject the claim.

Question 9

Which of the following best describes the p-value in hypothesis testing?

Accepted Answer

The probability of obtaining a test statistic as extreme as the observed value, assuming $$H_0 is $$true.

Question 10

A student calculates a test statistic $$t = -5.02$$ for a sample of 50 quarters. If the critical value for $$\alpha = 0.01 is$$ $$-2.405$$, what is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 11

Which of the following is a Type I error in the context of hypothesis testing?

Accepted Answer

Rejecting $$H_0$$ when $$H_0 is $$actually true.

Question 12

In the context of the sand timer experiment, which of the following would be an appropriate conclusion if the p-value is greater than $$\alpha$$?

Accepted Answer

Fail to reject $$H_0$$; there is not enough evidence to support the claim.

Question 13

Which of the following best describes the critical value in a $$t-$$test?

Accepted Answer

The value that separates the rejection region from the non-rejection region.

Question 14

A sample of 36 sand timer measurements has a mean of 178 seconds and a standard deviation of 5 seconds. Test the claim that the mean is not 180 seconds at $$\alpha = 0.05. $$What is the test statistic?

Accepted Answer

$$t = \frac{178 - 180}{5/\sqrt{36}}$$

Question 15

If the significance level $$\alpha is $$decreased from 0.05 to 0.01, what happens to the probability of making a Type I error?

Accepted Answer

It decreases.

Hypothesis Testing for a Population Mean (σ Unknown): Procedures, Examples, and Interpretation

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