Q: A survey of 565 adults found that 59% would erase their personal data online if they could. If the null hypothesis is $$H_0$$: p = 0.5$$, what is the value of the test statistic?

$$z = \dfrac{0.59 - 0.5}{\sqrt{\dfrac{0.5 \times 0.5}{565}}} = 4.28$$

Question 1

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

Accepted Answer

A statement that the value of a population parameter is equal to a specified value.

Question 2

A researcher claims that the mean weight of adult males in the US is less than 179 lbs. Which of the following correctly states the null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu = 179$$, H_a$$: \mu \u003c 179$$

Question 3

What is the significance level ($$\alpha) in $$hypothesis testing?

Accepted Answer

The probability of rejecting the null hypothesis when it is true.

Question 4

A survey of 565 adults found that 59% would erase their personal data online if they could. If the null hypothesis is $$H_0$$: p = 0.5$$, what is the value of the test statistic?

Accepted Answer

$$z = \dfrac{0.59 - 0.5}{\sqrt{\dfrac{0.5 	imes 0.5}{565}}} = 4.28$$

Question 5

In a right-tailed hypothesis test with $$\alpha = 0.05$$, what is the critical value for $$z$$?

Accepted Answer

$$z = 1.645$$

Question 6

Which of the following best describes a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 7

If the P-value for a right-tailed test is 0.0000 and $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Reject $$H_0.$$

Question 8

Which of the following statements about confidence intervals and hypothesis testing is correct?

Accepted Answer

If a confidence interval for a population parameter does not contain the claimed value, we should reject the claim.

Question 9

A left-tailed test is being conducted. Which of the following best describes the critical region?

Accepted Answer

The area in the left tail of the distribution.

Question 10

Suppose you are testing $$H_0$$: p = 0.87$$ versus H_a$$: p \u003e 0.87$$. Which of the following describes a Type II error in this context?

Accepted Answer

Failing to reject $$H_0$$ when the true proportion is greater than 0.87.

Question 11

Which of the following is the correct definition of the P-value in hypothesis testing?

Accepted Answer

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

Question 12

A two-tailed test is conducted at $$\alpha = 0.05. $$What is the total area of the critical region?

Accepted Answer

$$0.05$$

Question 13

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

Accepted Answer

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

Question 14

In a right-tailed test, the test statistic is $$z = 2.1$$ and the critical value is $$z = 1.645. $$What is the correct conclusion?

Accepted Answer

Reject $$H_0$$ because $$2.1 \u003e 1.645.$$

Question 15

Which of the following best describes the critical value in hypothesis testing?

Accepted Answer

The value of the test statistic that separates the region where we reject $$H_0$$ from the region where we do not reject $$H_0.$$

Question 16

A medical researcher is testing whether a new drug changes the mean recovery time from an illness. Which type of test should be used?

Accepted Answer

A two-tailed test

Question 17

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

Accepted Answer

It decreases.

Question 18

Which of the following is a correct non-technical conclusion for rejecting the null hypothesis in the context of a survey about erasing personal data online?

Accepted Answer

There is sufficient evidence to support the claim that most adults would erase their personal data online if they could.

Question 19

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

Accepted Answer

Type I error is rejecting a true null hypothesis, and Type II error is failing to reject a false null hypothesis.

Hypothesis Testing: Concepts, Procedures, and Applications

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