Q: A pharmaceutical company claims its new drug lowers systolic blood pressure by at least 5 mmHg compared to an old product. What is the appropriate null hypothesis ($$H_0) $$for this claim?

$$H_0$$: \mu_{\text{new}} - \mu_{\text{old}} \leq 5$$

Question 1

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

Accepted Answer

A claim that the observed effect is due to random chance.

Question 2

A pharmaceutical company claims its new drug lowers systolic blood pressure by at least 5 mmHg compared to an old product. What is the appropriate null hypothesis ($$H_0) $$for this claim?

Accepted Answer

$$H_0$$: \mu_{	ext{new}} - \mu_{	ext{old}} \leq 5$$

Question 3

Which of the following is an example of a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 4

Suppose a test has a significance level $$\alpha = 0.01. $$What does this mean?

Accepted Answer

There is a 1% chance of rejecting the null hypothesis when it is true.

Question 5

A manufacturer claims the mean weight of coffee in its packages is 500g. Customers suspect it is less. What is the appropriate alternative hypothesis ($$H_A$$)?

Accepted Answer

$$H_A: \mu \u003c 500$$

Question 6

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

Accepted Answer

The probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming $$H_0 is $$true.

Question 7

A study finds a p-value of 0.03 when testing whether a new fertilizer increases crop yield, using $$\alpha = 0.05. $$What is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is statistically significant evidence that the fertilizer increases yield.

Question 8

Which of the following statements about statistical significance and practical significance is correct?

Accepted Answer

A result can be statistically significant but not practically significant.

Question 9

In a two-tailed test, which of the following alternative hypotheses is appropriate?

Accepted Answer

$$H_A: \mu 
eq \mu_0$

Question 10

A researcher wants to know if a new teaching method changes average test scores compared to the current standard. Which test should be used?

Accepted Answer

A two-tailed test

Question 11

Which of the following steps is NOT part of the standard hypothesis testing procedure?

Accepted Answer

Accept the null hypothesis if the p-value is large

Question 12

A Type II error occurs when:

Accepted Answer

The null hypothesis is not rejected when it is false.

Question 13

If the power of a test is $$0.85$$, what does this mean?

Accepted Answer

There is an 85% chance of correctly rejecting the null hypothesis when it is false.

Question 14

Which of the following best describes a test statistic?

Accepted Answer

A numerical summary of the sample that is compared to a reference distribution under $$H_0.$$

Question 15

A researcher is testing whether the mean wait time in an emergency department is greater than 20 minutes. Which is the correct set of hypotheses?

Accepted Answer

$$H_0$$: \mu \leq 20,\ H_A: \mu \u003e 20$$

Question 16

Which of the following would increase the power of a statistical test?

Accepted Answer

Increasing the significance level $$\alpha$$

Question 17

A study reports a 95% confidence interval for the mean as (30.7, 38.4). What does this mean?

Accepted Answer

If we repeated the study many times, about 95% of the calculated intervals would contain the true mean.

Question 18

Which of the following is a correct interpretation of a non-significant p-value (e.g., $$p = 0.12) in a $$hypothesis test?

Accepted Answer

There is not enough evidence to reject the null hypothesis.

Question 19

A one-tailed test is most appropriate when:

Accepted Answer

You have a specific direction of interest for the effect.

Question 20

Which of the following is NOT a reason to use a two-tailed test?

Accepted Answer

You want to increase the power of the test.

Hypothesis Testing: The Basics

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