Q: A marketing company claims an 8% response rate to its mailings. In a sample of 500, 25 people respond. Test the claim at $$\alpha = 0.05. $$What is the value of the test statistic for the proportion?

$$z = \frac{0.05 - 0.08}{\sqrt{0.08 \times 0.92 / 500}} = -2.47$$

Question 1

Which of the following best describes the null hypothesis ($$H_0) in $$hypothesis testing?

Accepted Answer

A claim about a population parameter that represents the current belief or status quo.

Question 2

A Type I error in hypothesis testing occurs when:

Accepted Answer

You reject a true null hypothesis.

Question 3

Suppose a company claims that the mean weight of its cereal boxes is $$500$$ grams. A sample of $$36$$ boxes has a mean of $$495$$ grams and a known population standard deviation of $$12$$ grams. Test the claim at $$\alpha = 0.05. $$What is the value of the test statistic?

Accepted Answer

$$z = \frac{495 - 500}{12/\sqrt{36}} = -2.5$$

Question 4

Which of the following statements about the alternative hypothesis ($$H_1) is $$correct?

Accepted Answer

It is the hypothesis the researcher usually tries to prove.

Question 5

In a two-tailed hypothesis test with $$\alpha = 0.05$$, what are the critical z-values?

Accepted Answer

$$\pm 1.96$$

Question 6

A researcher is testing whether a new drug changes the average recovery time from a disease. The null hypothesis is $$H_0$$: \mu = 10$$ days. The sample mean is 8.5$ days, the sample standard deviation is 3$ days, and the sample size is 16$. What is the value of the t-statistic?

Accepted Answer

$$t = \frac{8.5 - 10}{3/\sqrt{16}} = -2.0$$

Question 7

Which of the following increases the probability of a Type II error ($$\beta$$), all else equal?

Accepted Answer

Decreasing the sample size ($$n)$$

Question 8

A marketing company claims an 8% response rate to its mailings. In a sample of 500, 25 people respond. Test the claim at $$\alpha = 0.05. $$What is the value of the test statistic for the proportion?

Accepted Answer

$$z = \frac{0.05 - 0.08}{\sqrt{0.08 	imes 0.92 / 500}} = -2.47$$

Question 9

Which of the following is NOT an assumption for using the t-test for the mean?

Accepted Answer

The population standard deviation is known.

Question 10

If the p-value for a hypothesis test is 0.045 and $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 11

Which of the following best describes the power of a statistical test?

Accepted Answer

The probability of rejecting $$H_0$$ when $$H_0 is $$false.

Question 12

A business wants to test if the average delivery time is less than 4.5 minutes. Which is the correct set of hypotheses?

Accepted Answer

$$H_0$$: \mu \geq 4.5$$, H_1$: \mu \u003c 4.5$$

Question 13

Which of the following is a possible consequence of violating the normality assumption in a t-test?

Accepted Answer

The test statistic may not follow the t-distribution, leading to incorrect conclusions.

Question 14

Which of the following is true about statistical significance and practical significance?

Accepted Answer

Statistically significant results may not always be practically significant, especially with large sample sizes.

Question 15

A sample of 25 hotels in New York has a mean room rate of $$172.50$$ and a sample standard deviation of $$15.40. $$The hypothesized mean is $$168. At$$ $$\alpha = 0.05$$, what is the critical value for a two-tailed t-test?

Accepted Answer

$$\pm 2.064$$

Question 16

Which of the following is an ethical issue in hypothesis testing?

Accepted Answer

Failing to report non-significant results.

Question 17

If $$\alpha is $$decreased from $$0.05 to$$ $$0.01$$, what happens to the probability of a Type II error ($$\beta$$), all else equal?

Accepted Answer

$$\beta$$ increases

Question 18

Which formula is used to calculate the test statistic for a hypothesis test for a population mean when the population standard deviation is unknown?

Accepted Answer

$$t_{STAT} = \frac{\overline{X} - \mu}{S/\sqrt{n}}$$

Step-by-Step Guidance for Hypothesis Testing (Z-Test for Mean)

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