Question 1

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

Accepted Answer

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

Question 2

A researcher claims that a new medication increases the average recovery rate. Which is the correct symbolic form for the alternative hypothesis ($$H_1) if $$the current average recovery rate is $$ar{x} = 0.5$$?

Accepted Answer

$$H_1$$: ar{x} \u003e 0.5$$

Question 3

In a right-tailed hypothesis test for a population proportion, which of the following is the correct critical region?

Accepted Answer

The area in the extreme right tail under the curve.

Question 4

Suppose you are testing the claim that the proportion of students using online textbooks is less than 0.6. What is the correct null hypothesis ($$H_0$$)?

Accepted Answer

$$H_0$$: p = 0.6$$

Question 5

Which of the following statements about the significance level ($$\alpha) is $$correct?

Accepted Answer

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

Question 6

A sample of 926 internet users finds that 482 use two-factor authentication. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{482}{926}$$

Question 7

Given $$n = 926$$, $$p = 0.5$$, and $$q = 0.5$$, which requirement must be satisfied to use the normal distribution for testing a proportion?

Accepted Answer

$$np \u003e 5$$ and $$nq \u003e 5$$

Question 8

What is the formula for the test statistic $$z$$ when testing a claim about a population proportion?

Accepted Answer

$$z = \frac{\hat{p} - p}{\sqrt{pq/n}}$$

Question 9

If the P-value for a test is 0.106 and the significance level $$\alpha is 0.05$$, what is the correct decision?

Accepted Answer

Fail to reject the null hypothesis.

Question 10

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

Accepted Answer

Rejecting a true null hypothesis.

Question 11

A medical procedure is claimed to increase the probability of a baby girl ($$p \u003e 0.5). $$Which scenario describes a Type II error?

Accepted Answer

In reality $$p \u003e 0.5$$, but we fail to support that conclusion.

Question 12

What is the power of a hypothesis test?

Accepted Answer

The probability of rejecting a false null hypothesis.

Question 13

Which of the following is a common requirement for the power of a hypothesis test when designing an experiment?

Accepted Answer

Power of at least 0.80

Question 14

If a confidence interval for a population mean does not include the claimed value, what should you conclude?

Accepted Answer

Reject the claim.

Question 15

Which of the following is true about the equivalence of confidence intervals and hypothesis tests?

Accepted Answer

Confidence intervals and hypothesis tests always lead to the same conclusion for means.

Question 16

A researcher wants to detect a reduction in the coronary heart disease rate from 0.5 to 0.4 with 80% power and $$\alpha = 0.05. $$What is the minimum sample size required according to the study material?

Accepted Answer

At least 153 subjects

Question 17

Which of the following is the correct formula for the test statistic $$t$$ when testing a claim about a mean with unknown population standard deviation?

Accepted Answer

$$t = \frac{\bar{x} - \mu}{s/\sqrt{n}}$$

Question 18

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

Accepted Answer

Calculate the sample mean

Question 19

In the context of hypothesis testing, why is the phrase 'fail to reject the null hypothesis' preferred over 'accept the null hypothesis'?

Accepted Answer

Because 'accept' implies the null hypothesis is proven, which is not possible.

Chapter 8: Hypothesis Testing – Structured Study Notes

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