Question 1

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 2

In the context of a criminal trial, what does the null hypothesis ($$H_0) $$represent?

Accepted Answer

The defendant is innocent.

Question 3

If the probability of making a Type I error is $$\alpha = 0.05$$, what is the probability of making a Type II error if the two probabilities are inversely related and must sum to 1?

Accepted Answer

$$\beta = 0.95$$

Question 4

Which of the following statements about the power of a statistical test is correct?

Accepted Answer

Power is the probability of correctly rejecting the null hypothesis.

Question 5

A researcher wants to test if the mean number of diseased koalas differs between urban and rural areas. Which is the correct alternative hypothesis ($$H_A) $$for a two-tailed test?

Accepted Answer

$$H_A: \mu_R 
eq \mu_U$$

Question 6

Which formula is used to calculate the Pearson’s chi-square test statistic?

Accepted Answer

$$T = \sum_{i=1}^k \frac{(O - E)^2$}{E}$$

Question 7

In a chi-square goodness of fit test, what does the degrees of freedom (df) represent?

Accepted Answer

The number of categories minus one.

Question 8

A school administrator wants to determine if there is an association between students' favorite subjects and their grade levels. What is the null hypothesis ($$H_0) $$for this chi-square test of independence?

Accepted Answer

Favorite subjects and grade levels are independent.

Question 9

If the calculated chi-square test statistic is less than the critical value from the chi-square table, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis.

Question 10

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

Accepted Answer

The probability of observing a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true.

Question 11

A left-tail test is appropriate when the alternative hypothesis is:

Accepted Answer

$$H_A: \mu \u003c \mu_0$

Question 12

In the Gold Lotto example, if the calculated test statistic is $$T = 31$$ and the critical value at $$\alpha = 0.05 is$$ $$67.5$$, what is the correct statistical conclusion?

Accepted Answer

Fail to reject the null hypothesis; the selection is fair.

Question 13

Which of the following is NOT a requirement for a good sample in statistical inference?

Accepted Answer

The sample should be as small as possible.

Question 14

What is the main difference between a one-tail and a two-tail hypothesis test?

Accepted Answer

A one-tail test only considers deviations in one direction from the null hypothesis, while a two-tail test considers deviations in both directions.

Question 15

Which of the following best describes the acceptance region in hypothesis testing?

Accepted Answer

The range of values for which the null hypothesis is not rejected.

Question 16

In a chi-square test of independence, how do you calculate the expected frequency for a cell in a contingency table?

Accepted Answer

$$\frac{	ext{Row Total} 	imes 	ext{Column Total}}{	ext{Grand Total}}$$

Question 17

Which of the following is true about Pearson’s correlation coefficient?

Accepted Answer

It can be negative or positive.

Question 18

If you want to minimize the risk of a Type I error in a life-or-death situation, such as a murder trial, which significance level ($$\alpha) $$would you choose?

Accepted Answer

$$\alpha = 0.01$$

Question 19

Which of the following is a correct interpretation if the p-value is less than the significance level ($$\alpha$$)?

Accepted Answer

Reject the null hypothesis.

Statistical Inference and Hypothesis Testing: Concepts and Applications

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