Q: A university wants to test if the average GPA of its students has changed from the previous year's mean of 3.2. Which of the following correctly states the null and alternative hypotheses?

$$H_0$$: \mu = 3.2$$ H_a$$: \mu \neq 3.2$$

Q: A two-tailed test is performed with $$z = -2.5. $$What is the P-value?

P-value = $$2 \times 0.0062 = 0.0124$$

Question 1

A university wants to test if the average GPA of its students has changed from the previous year's mean of 3.2. Which of the following correctly states the null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu = 3.2$$ 
H_a$$: \mu 
eq 3.2$$

Question 2

A hospital claims that the average wait time in its emergency room is less than 30 minutes. Which is the correct set of hypotheses for testing this claim?

Accepted Answer

$$H_0$$: \mu = 30$$ 
H_a$$: \mu \u003c 30$$

Question 3

A researcher claims that the proportion of people in a city who recycle is more than 60%. Which of the following is the correct null and alternative hypothesis?

Accepted Answer

$$H_0$$: p = 0.60$$ 
H_a$$: p \u003e 0.60$$

Question 4

A pharmaceutical company claims that the standard deviation of the active ingredient in its pills is 2 mg. A hypothesis test is conducted and the null hypothesis is not rejected. What is the correct interpretation?

Accepted Answer

There is not sufficient sample evidence to support the claim that the standard deviation is different from 2 mg.

Question 5

A cereal company claims the mean weight of its cereal boxes is at least 16 ounces. A hypothesis test leads to rejection of the null hypothesis. What is the correct conclusion in nontechnical terms?

Accepted Answer

There is not sufficient sample evidence to support the claim that the mean weight is at least 16 ounces.

Question 6

A sample of 40 patients has a mean recovery time of 12 days with a population standard deviation of 4 days. The hospital claims the mean recovery time is less than 14 days. What is the value of the test statistic $$z$$?

Accepted Answer

$$z = \frac{12 - 14}{\frac{4}{\sqrt{40}}} = -3.16$$

Question 7

A right-tailed hypothesis test is conducted with $$z = 2.0$$ and $$\alpha = 0.05. $$What is the P-value and is the alternative hypothesis supported?

Accepted Answer

P-value = $$0.0228$$; alternative hypothesis is supported.

Question 8

A two-tailed test is performed with $$z = -2.5. $$What is the P-value?

Accepted Answer

P-value = $$2 	imes 0.0062 = 0.0124$$

Question 9

A sample of 50 batteries has a mean life of 98 hours. The population mean is 100 hours and the standard deviation is 10 hours. What is the $$z-$$score for this sample mean?

Accepted Answer

$$z = \frac{98 - 100}{\frac{10}{\sqrt{50}}} = -1.41$$

Question 10

A left-tailed test is conducted with $$z = -1.5$$ and $$\alpha = 0.05. $$What is the P-value and is the alternative hypothesis supported?

Accepted Answer

P-value = $$0.0668$$; alternative hypothesis is not supported.

Question 11

A sample of 32 students at a high school has a mean weekly TV watching time of 19.8 hours. The city average is 22 hours, and the population standard deviation is 7.2 hours. Test the claim that the mean at this school is less than the city average at $$\alpha = 0.05.$$

Accepted Answer

Supported; $$z = \frac{19.8 - 22}{\frac{7.2}{\sqrt{32}}} = -1.73$$, which is less than $$-1.645.$$

Question 12

A sample of 70 students has a mean SAT score of 469. The 1990 mean was 475, with a population standard deviation of 73. Test the claim that the mean has dropped at $$\alpha = 0.05.$$

Accepted Answer

Not supported; $$z = \frac{469 - 475}{\frac{73}{\sqrt{70}}} = -0.69$$, which is not less than $$-1.645.$$

Question 13

In a hypothesis test, what is a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is actually true.

Question 14

In a hypothesis test, what is a Type II error?

Accepted Answer

Failing to reject the null hypothesis when it is actually false.

Question 15

A medical school claims that more than 28% of its students plan to go into general practice. In a sample of 130 students, 32% plan to go into general practice. What is the P-value for this right-tailed test?

Accepted Answer

P-value = $$0.1539$$

Question 16

A manufacturer claims that fewer than 6% of its fax machines are defective. In a sample of 97, 5% are defective. What is the P-value for this left-tailed test?

Accepted Answer

P-value = $$0.3409$$

Question 17

A random sample of 139 forty-year-old men contains 26% who smoke. Test the claim that the percentage of forty-year-old men that smoke is 22%. What is the P-value for this two-tailed test?

Accepted Answer

P-value = $$0.2542$$

Question 18

A supplier claims that no more than 1% of 3.5" disks are defective. In a sample of 800 disks, 3% are defective. At $$\alpha = 0.05$$, is the supplier's claim supported?

Accepted Answer

Not supported; the sample provides enough evidence to reject the claim.

Question 19

In a sample of 47 adults, 8 have been exposed to a particular flu strain. Test the claim that the proportion of all adults exposed is different from 8%. At $$\alpha = 0.05$$, is the claim supported?

Accepted Answer

Not supported; the sample does not provide enough evidence to reject the null hypothesis.

STA1013 Chapter 9 Review – Hypothesis Testing and Statistical Inference Guidance

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