Q: Which of the following is the correct formula for the probability of making a Type II error?

$$\beta = P(\text{Fail to reject } H_0$ \mid H_a \text{ is true})$$

Q: A sample proportion is found to be 0.44, while the hypothesized population proportion is 0.42. The sample size is 220. What is the value of the test statistic?

$$z = \frac{0.44 - 0.42}{\sqrt{\frac{0.42 \times 0.58}{220}}}$$

Question 1

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

Accepted Answer

It is a statement that the population parameter is equal to a specific value.

Question 2

A researcher wants to test whether the mean amount of time employees spend on social media during work hours is different from 1.5 hours. What is the appropriate null hypothesis?

Accepted Answer

$$H_0$$: \mu = 1.5$$

Question 3

Which error occurs when the null hypothesis is rejected even though it is actually true?

Accepted Answer

Type I Error

Question 4

Suppose a survey finds that 42% of males say their favorite color is blue. You want to test if the proportion of college-age males whose favorite color is blue is different from 42%. What is the alternative hypothesis?

Accepted Answer

$$H_a: p 
eq 0.42$$

Question 5

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

Accepted Answer

$$z = \frac{\hat{p} - p_0$}{\sqrt{\frac{p_0$(1-p_0$)}{n}}}$$

Question 6

A manufacturer claims the standard deviation of fill volumes for a drink is 0.81 liters. A sample of 20 bottles has a sample standard deviation of 0.73 liters. Which test should be used to evaluate the claim?

Accepted Answer

A hypothesis test for a population standard deviation using the chi-square distribution

Question 7

If the significance level ($$\alpha) is $$increased, what happens to the probability of making a Type I error?

Accepted Answer

It increases

Question 8

Which of the following is the correct formula for the probability of making a Type II error?

Accepted Answer

$$\beta = P(	ext{Fail to reject } H_0$ \mid H_a 	ext{ is true})$$

Question 9

A fast-food restaurant manager wants to test if the average bill per car passing through the drive-thru is greater than $12.50. What type of hypothesis test should be performed?

Accepted Answer

Right-tailed test for a population mean

Question 10

Which of the following statements best describes practical significance?

Accepted Answer

It refers to results that are statistically significant but may not be important in real-world terms.

Question 11

In hypothesis testing for a population mean, which formula is used for the test statistic when the population standard deviation is known?

Accepted Answer

$$z = \frac{\bar{x} - \mu_0$}{\frac{\sigma}{\sqrt{n}}}$$

Question 12

A sample proportion is found to be 0.44, while the hypothesized population proportion is 0.42. The sample size is 220. What is the value of the test statistic?

Accepted Answer

$$z = \frac{0.44 - 0.42}{\sqrt{\frac{0.42 	imes 0.58}{220}}}$$

Question 13

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

Accepted Answer

Calculate the population mean

Question 14

When testing hypotheses about a population proportion using the binomial probability distribution, which condition must be met for the normal approximation to be valid?

Accepted Answer

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

Question 15

A Type II error occurs when:

Accepted Answer

The null hypothesis is not rejected when it is false

Question 16

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

Accepted Answer

The probability of obtaining a sample statistic as extreme as the observed, assuming the null hypothesis is true

Question 17

A researcher wants to test if the mean age at first childbirth has increased from 25.2 years. A random sample of 1200 women has a mean age of 25.5 years and a standard deviation of 4.6 years. What is the null hypothesis?

Accepted Answer

$$H_0$$: \mu = 25.2$$

Question 18

Which of the following is a characteristic of the chi-square distribution?

Accepted Answer

It is always positively skewed

Question 19

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

Accepted Answer

The probability of making a Type I error

Hypothesis Tests Regarding a Parameter: Concepts, Procedures, and Applications

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