Question 1

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

Accepted Answer

A statement of no change, no effect, or no difference, assumed true until evidence indicates otherwise.

Question 2

A researcher claims that the mean length of a phone call has increased since 2006, when it was 3.25 minutes. Which are the correct null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu = 3.25$$; H_1$: \mu \u003e 3.25$$

Question 3

What is a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when the null hypothesis is true.

Question 4

In the context of hypothesis testing, what does the level of significance ($$\alpha) $$represent?

Accepted Answer

The probability of making a Type I error.

Question 5

A sample of 1000 people yields a sample proportion $$\hat{p} = 0.534$$ for favoring a policy. If the population proportion is $$p = 0.5$$, what is the z-score for this sample proportion?

Accepted Answer

$$z = \frac{0.534 - 0.5}{\sqrt{0.5(1-0.5)/1000}} = 2.15$$

Question 6

Which of the following is true about the power of a statistical test?

Accepted Answer

It is the probability of rejecting the null hypothesis when the alternative hypothesis is true.

Question 7

If a hypothesis test for a population mean uses the t-distribution, which condition must be met?

Accepted Answer

The population standard deviation must be unknown.

Question 8

A sociologist claims that births to mothers under 20 years of age are decreasing. In a sample of 34 births, 3 were to mothers under 20. If the population proportion in 2006 was 0.105, which test should be used?

Accepted Answer

A binomial probability test, since $$np_0(1$$-$$p_0$$) \u003c 10$$

Question 9

Which of the following best describes practical significance?

Accepted Answer

A result is statistically significant but the difference is not large enough to be considered important in real life.

Question 10

For a hypothesis test about a population standard deviation, which distribution is used for the test statistic?

Accepted Answer

Chi-square distribution

Question 11

A quality control manager believes the standard deviation of wine bottles has decreased with new equipment. What are the correct hypotheses?

Accepted Answer

$$H_0$$: \sigma = 0.23$$; H_1$: \sigma \u003c 0.23$$

Question 12

In a right-tailed test for a population proportion, which criterion is used to reject the null hypothesis?

Accepted Answer

If $$z_0$$ \u003e z_\alpha$$

Question 13

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

Accepted Answer

$$t_0$$ = \frac{x - \$$mu_0$$}{s / \sqrt{n}}$$

Question 14

A hypothesis test yields a P-value of 0.0158. If the significance level is $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 15

Which of the following is NOT a requirement for using the normal model to describe the sampling distribution of the sample proportion?

Accepted Answer

The sample size must be at least 30.

Question 16

If the probability of a Type II error ($$\beta) is 0.1539$$, what is the power of the test?

Accepted Answer

$$1 - \beta = 0.8461$$

Question 17

A boxplot of state quarter weights shows no outliers and a roughly symmetric distribution. What does this suggest about the appropriateness of using a t-test for the mean?

Accepted Answer

The t-test is appropriate because the data are approximately normal and have no outliers.

Question 18

Which formula is used to calculate the test statistic for a population standard deviation?

Accepted Answer

$$\$$chi^2$$_0 = \frac{(n-1)s^2$}{\$$sigma_0$$^2}$$

Hypothesis Testing: Concepts, Procedures, and Applications

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