Q: Suppose you are testing $$H_0$$: p = 0.5$$ for a proportion, and you observe 87 successes out of 100 trials. What is the test statistic?

$$z = \frac{0.87 - 0.5}{\sqrt{0.5 \times 0.5 / 100}}$$

Question 1

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

Accepted Answer

It is a statement that will be accepted unless the data provide convincing evidence that it is false.

Question 2

A medical researcher claims that the mean body temperature of healthy adults is equal to 98.6°F. What is the appropriate null hypothesis ($$H_0) $$for this claim?

Accepted Answer

$$H_0$$: \mu = 98.6$$

Question 3

Which of the following is the correct formula for the test statistic for a sample mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

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

Question 4

A manufacturer wants to test if the mean fill of its bottles is 12 ounces. A sample of 100 bottles has a mean of 12.1 ounces and a standard deviation of 0.76 ounces. What is the correct test statistic to use?

Accepted Answer

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

Question 5

If the significance level $$\alpha is $$set to 0.01, what does this mean in the context of hypothesis testing?

Accepted Answer

There is a 1% chance of rejecting the null hypothesis when it is true (Type I error).

Question 6

Which of the following statements about the P-value is correct?

Accepted Answer

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

Question 7

A sample of 100 bearings from a production line has a mean diameter of 5.06 inches and a standard deviation of 0.48 inches. The null hypothesis is $$H_0$$: \mu = 5$$. Calculate the z$-test statistic.

Accepted Answer

$$z = \frac{5.06 - 5}{0.48 / \sqrt{100}} = 1.25$$

Question 8

Which of the following is a correct step in performing a hypothesis test for a population mean when the sample size is small and the population standard deviation is unknown?

Accepted Answer

Use the $$t-$$test statistic.

Question 9

In a two-tailed hypothesis test, which of the following best describes the rejection region?

Accepted Answer

It is in both the left and right tails of the sampling distribution.

Question 10

Suppose you are testing $$H_0$$: p = 0.5$$ for a proportion, and you observe 87 successes out of 100 trials. What is the test statistic?

Accepted Answer

$$z = \frac{0.87 - 0.5}{\sqrt{0.5 	imes 0.5 / 100}}$$

Question 11

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

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 12

A researcher wants to test if the mean score of a new drug is greater than 50. Which of the following is the correct alternative hypothesis ($$H_a$$)?

Accepted Answer

$$H_a: \mu \u003e 50$$

Question 13

When performing a hypothesis test for a population proportion, which condition must be met to use the $$z-$$test statistic?

Accepted Answer

You must have at least 5 successes and at least 5 failures in your sample.

Question 14

A tobacco company claims that fewer than 40% of cigarette consumers fail to see the warning. What is the correct null hypothesis ($$H_0) $$for this test?

Accepted Answer

$$H_0$$: p = 0.4$$

Question 15

If the sample size is small ($$n \u003c 30) $$and the population standard deviation is unknown, which distribution should be used for the test statistic?

Accepted Answer

t-distribution

Question 16

Which of the following best describes the power of a statistical test?

Accepted Answer

The probability of correctly rejecting the null hypothesis when it is false.

Question 17

A test statistic is calculated as $$z = 2.91. If $$the critical value for a two-tailed test at $$\alpha = 0.01 is$$ $$\pm 2.576$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 18

Which of the following is the correct formula for the test statistic for a sample proportion?

Accepted Answer

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

Question 19

In hypothesis testing, what is the main purpose of setting a significance level ($$\alpha$$)?

Accepted Answer

To set the threshold for rejecting the null hypothesis.

Chapter 8: Hypothesis Testing – Structured Study Notes

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