Question 1

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

Accepted Answer

It is a claim about a population parameter that represents the current belief.

Question 2

A researcher wants to test if the average monthly cell phone bill in a city is different from $$\42$. Which of the following is the correct alternative hypothesis (H_1$)?

Accepted Answer

$$H_1$$: \mu 
eq 42$$

Question 3

In hypothesis testing, what does a Type I error represent?

Accepted Answer

Rejecting a true null hypothesis.

Question 4

Suppose a company claims that 8% of its customers respond to a mailing. In a sample of 500, 25 respond. What is the value of the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = 0.05$$

Question 5

Which formula is used to calculate the test statistic for a one-sample Z-test for the mean when population standard deviation $$\sigma is $$known?

Accepted Answer

$$Z = \dfrac{\bar{x} - \mu}{\sigma / \sqrt{n}}$$

Question 6

A sample of 25 hotels in New York has a mean room rate of $$\172.50$ and a sample standard deviation of $$\$$15.40. $$Test the claim that the population mean is $$\168$ using a two-tailed t-test at $$\alpha = 0.05$. What is the value of the test statistic?

Accepted Answer

$$t = \dfrac{172.50 - 168}{15.40 / \sqrt{25}} = 1.46$$

Question 7

Which of the following is NOT an assumption for using the t-test for the mean when $$\sigma is $$unknown?

Accepted Answer

The population standard deviation is known.

Question 8

If the p-value for a hypothesis test is $$0.0456$$ and the significance level $$\alpha is$$ $$0.05$$, what is the correct decision?

Accepted Answer

Reject the null hypothesis.

Question 9

Which of the following statements about Type I and Type II errors is TRUE?

Accepted Answer

Type I error can only occur if $$H_0 is $$true.

Question 10

A manager claims that the average monthly cell phone bill is over $$\52$. A sample of 25 bills has a mean of $$\$$53.10$$ and a standard deviation of $$\10$. What is the test statistic for an upper-tail t-test?

Accepted Answer

$$t = \dfrac{53.10 - 52}{10 / \sqrt{25}} = 0.55$$

Question 11

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

Accepted Answer

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

Question 12

When conducting a hypothesis test for a proportion, which condition must be met for the normal approximation to be valid?

Accepted Answer

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

Question 13

Which of the following is a potential ethical issue in hypothesis testing?

Accepted Answer

Reporting only statistically significant results.

Question 14

A two-tailed test for the mean with $$\alpha = 0.05$$ has critical Z values of $$\pm 1.96. If $$the calculated test statistic is $$Z = -2.0$$, what is the correct conclusion?

Accepted Answer

Reject $$H_0.$$

Question 15

Which of the following best explains the difference between statistical significance and practical significance?

Accepted Answer

Statistical significance means the result is unlikely due to chance, but it may not be important in practice.

Question 16

If the population standard deviation $$\sigma is $$unknown, which distribution should be used for hypothesis testing about the mean?

Accepted Answer

t distribution.

Question 17

Which of the following factors will decrease the probability of a Type II error ($$\beta$$)?

Accepted Answer

Increasing the difference between the hypothesized and true parameter values.

Question 18

A confidence interval for the mean is calculated as $$\bar{x} \pm Z_{\alpha/2} \dfrac{\sigma}{\sqrt{n}}. If $$the interval does NOT contain the hypothesized mean, what does this imply about the hypothesis test at significance level $$\alpha$$?

Accepted Answer

Reject the null hypothesis.

Question 19

Which of the following is NOT a step in the hypothesis testing process?

Accepted Answer

Always accept the null hypothesis if the p-value is less than $$\alpha.$$

Fundamentals of Hypothesis Testing: One-Sample Tests (Business Statistics, Chapter 9)

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