Question 1

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

Accepted Answer

A statement about the population parameter that is assumed to be true unless there is strong evidence against it.

Question 2

A tire manufacturer claims their new tire design lasts more than 60,000 miles. Which is the correct way to set up the null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu \leq 60,000$$ miles; H_A$$: \mu \u003e 60,000$$ miles

Question 3

In the context of hypothesis testing, what is a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 4

A company claims their average service time is 40 minutes or less. A sample of 100 services has a mean of 43.5 minutes and a known population standard deviation of 8 minutes. What is the value of the z-test statistic?

Accepted Answer

$$z = \frac{43.5 - 40}{8/\sqrt{100}} = 4.375$$

Question 5

Which of the following statements about the significance level ($$\alpha) is $$correct?

Accepted Answer

It is the maximum allowable probability of committing a Type I error.

Question 6

A sample of 64 homes has a mean framing and roofing time of 26 days. The population standard deviation is 3 days, and the hypothesized mean is 25 days. What is the z-test statistic?

Accepted Answer

$$z = \frac{26 - 25}{3/\sqrt{64}} = 2.67$$

Question 7

In a two-tailed hypothesis test with $$\alpha = 0.05$$ and $$n = 16$$, what are the critical t-values?

Accepted Answer

$$t = \pm 2.131$$

Question 8

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

Accepted Answer

The probability, assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as the one calculated from the sample.

Question 9

A marketing manager wants to test if more than 10% of season ticket holders will cancel their orders after a price increase. In a sample of 100, 14 say they would cancel. What is the sample proportion?

Accepted Answer

$$\hat{p} = 0.14$$

Question 10

Which of the following is a requirement for using the z-test for proportions?

Accepted Answer

$$np \geq 5$$ and $$n(1-p) \geq 5$$

Question 11

A business wants to test if the mean waiting time at a clinic is less than 15 minutes. Which is the correct alternative hypothesis?

Accepted Answer

$$H_A: \mu \u003c 15$$

Question 12

If the p-value is greater than the significance level $$\alpha$$, what is the correct decision?

Accepted Answer

Do not reject the null hypothesis.

Question 13

Which Excel function can be used to find the critical value for a one-tailed z-test with $$\alpha = 0.10$$, mean $$= 25$$, and standard error $$= 3/\sqrt{64}$$?

Accepted Answer

=NORM.INV(0.9, 25, 3/\sqrt{64})

Question 14

A hypothesis test for a mean with $$\sigma$$ known uses the following formula for the test statistic. Which is correct?

Accepted Answer

$$z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$$

Question 15

In a criminal trial, the null hypothesis is that the defendant is innocent. If the jury convicts an innocent person, what type of error has occurred?

Accepted Answer

Type I error

Question 16

A two-tailed test is being conducted at $$\alpha = 0.05. $$What is the total area in both rejection regions combined?

Accepted Answer

0.05

Question 17

Which of the following is NOT a correct statement about the alternative hypothesis ($$H_A$$)?

Accepted Answer

It always contains an equality sign.

Question 18

A sample of 16 ice cream cartons is tested for mean fill. The test is two-tailed with $$\alpha = 0.05. $$What is the correct decision rule using the t-distribution?

Accepted Answer

Reject $$H_0 if$$ $$t  2.131$$

Question 19

If a business wants to minimize the chance of a Type I error, what should they do?

Accepted Answer

Decrease the significance level $$\alpha$$

Chapter 9: Introduction to Hypothesis Testing – Business Statistics Study Notes

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