Q: A sample of 200 adults is surveyed, and 120 say they would erase all their personal information online if they could. Test the claim that more than 50% of adults would do so. What is the value of the test statistic?

$$z = \frac{0.60 - 0.50}{\sqrt{\frac{0.5 \times 0.5}{200}}} = \frac{0.10}{0.0354} \approx 2.83$$

Question 1

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

Accepted Answer

A statement that the value of a population parameter is equal to some claimed value.

Question 2

A researcher claims that the average commute time in a city is less than 30 minutes. Which of the following correctly expresses the null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu = 30$$, H_1$: \mu \u003c 30$$

Question 3

What is the significance level $$\alpha in $$hypothesis testing?

Accepted Answer

The probability of rejecting $$H_0$$ when $$H_0 is $$true.

Question 4

A sample of 100 college students has a mean IQ score of 110 with a known population standard deviation of 15. Test the claim that the population mean is 105 using $$\alpha = 0.05. $$What is the value of the test statistic?

Accepted Answer

$$z = \frac{110 - 105}{15/\sqrt{100}} = \frac{5}{1.5} = 3.33$$

Question 5

Which of the following is true about the P-value in hypothesis testing?

Accepted Answer

It is the probability of obtaining a test statistic at least as extreme as the one observed, assuming $$H_0 is $$true.

Question 6

A right-tailed test is being conducted. The test statistic is $$z = 2.10. $$What is the P-value?

Accepted Answer

P-value = area to the right of $$z = 2.10$$

Question 7

Which test statistic formula should be used to test a claim about a population proportion $$p$$?

Accepted Answer

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

Question 8

A pharmaceutical company claims that their new drug reduces blood pressure with a standard deviation greater than 5 mm Hg. A sample of 50 patients has a sample standard deviation of 7 mm Hg. Which test statistic should be used?

Accepted Answer

$$\$$chi^2$$ = \frac{(n-1)s^2$}{\$$sigma^2$$}$$

Question 9

If the P-value is 0.03 and the significance level $$\alpha is 0.05$$, what is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 10

A two-tailed test is being conducted at $$\alpha = 0.01. $$What is the critical value for $$z$$?

Accepted Answer

$$z = \pm 2.575$$

Question 11

A sample of 200 adults is surveyed, and 120 say they would erase all their personal information online if they could. Test the claim that more than 50% of adults would do so. What is the value of the test statistic?

Accepted Answer

$$z = \frac{0.60 - 0.50}{\sqrt{\frac{0.5 	imes 0.5}{200}}} = \frac{0.10}{0.0354} \approx 2.83$$

Question 12

Which of the following best describes a left-tailed test?

Accepted Answer

The critical region is in the extreme left tail under the curve.

Question 13

A hypothesis test results in a P-value of 0.12. If $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Fail to reject $$H_0$$

Question 14

Which of the following is the correct symbolic form for the alternative hypothesis when testing if a population mean is not equal to 100?

Accepted Answer

$$H_1$$: \mu 
eq 100$$

Question 15

A test statistic falls in the critical region. What is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 16

A left-tailed test is being conducted. The test statistic is $$z = -1.75. $$What is the P-value?

Accepted Answer

P-value = area to the left of $$z = -1.75$$

Question 17

Which of the following is NOT a possible conclusion in hypothesis testing?

Accepted Answer

There is sufficient evidence to prove the null hypothesis is true.

Chapter 8: Hypothesis Testing – Structured Study Notes

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