Question 1

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

Accepted Answer

A statement of no effect, no difference, or no change in the population parameter.

Question 2

A pharmaceutical company tests whether a new drug reduces blood pressure more than the current standard. Which is the correct formulation of the null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu_{new} = \mu_{standard}$$; H_A$$: \mu_{new} \u003e \mu_{standard}$$

Question 3

Which of the following is a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is actually true.

Question 4

A coffee company claims their packages contain 500g of coffee. A consumer group suspects the packages weigh less. What is the correct alternative hypothesis for a one-sided test?

Accepted Answer

$$H_A: \mu \u003c 500$$

Question 5

In hypothesis testing, what does the p-value represent?

Accepted Answer

The probability of obtaining a result as extreme as the observed, assuming the null hypothesis is true.

Question 6

If a test is conducted at significance level $$\alpha = 0.05$$, what does this mean?

Accepted Answer

There is a 5% chance of rejecting the null hypothesis when it is true.

Question 7

A biologist is testing whether a gene is differentially expressed (could be up-regulated or down-regulated) in treated cells compared to controls. Which type of test should be used?

Accepted Answer

A two-tailed test

Question 8

Which of the following statements about the alternative hypothesis $$H_A is $$correct?

Accepted Answer

It is the hypothesis that researchers hope to support, suggesting a parameter is different from the null value.

Question 9

Suppose a test statistic yields a p-value of 0.03. If the significance level is $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Reject the null hypothesis.

Question 10

Which of the following best describes statistical power ($$1 - \beta$$)?

Accepted Answer

The probability of correctly rejecting the null hypothesis when the alternative is true.

Question 11

A researcher is only interested in whether a new fertilizer increases plant height, not decreases it. Which is the correct alternative hypothesis?

Accepted Answer

$$H_A: \mu \u003e \mu_0$

Question 12

Which of the following is a common misconception about the p-value?

Accepted Answer

It is the probability that the null hypothesis is true.

Question 13

In a medical trial, a Type II error would mean:

Accepted Answer

Failing to detect that a new drug improves symptoms when it actually does.

Question 14

Which of the following increases the power of a statistical test?

Accepted Answer

Increasing the significance level $$\alpha.$$

Question 15

A manufacturer wants to test if the mean weight of their product is different from 500g. Which is the correct alternative hypothesis for a two-tailed test?

Accepted Answer

$$H_A: \mu 
eq 500$$

Question 16

Why do statisticians say we 'never accept' the null hypothesis?

Accepted Answer

Because failing to reject $$H_0$$ does not prove it is true; it only means there is not enough evidence against it.

Question 17

A business analyst wants to minimize the risk of missing a true effect (Type II error). Which of the following should they do?

Accepted Answer

Increase the sample size.

Question 18

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

Accepted Answer

Accept the null hypothesis if the p-value is large.

Question 19

A Type I error in a court analogy is most similar to:

Accepted Answer

Convicting an innocent defendant.

Question 20

If the probability of a Type II error ($$\beta) is 0.20$$, what is the power of the test?

Accepted Answer

$$0.80$$

Chapter 10 Hypothese

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