Question 1

A pharmaceutical company claims that less than 10% of patients experience side effects from a new drug. A hypothesis test is conducted and the null hypothesis is rejected at the 0.05 significance level. What is the correct nontechnical conclusion?

Accepted Answer

There is sufficient evidence to support the claim that less than 10% of patients experience side effects.

Question 2

Given a right-tailed test with a test statistic $$z = 1.25$$, what is the P-value? Use the standard normal distribution.

Accepted Answer

$$0.1056$$

Question 3

A researcher tests $$H_0$$: \mu = 50$$ versus H_1$: \mu 
eq 50$$ using a sample of $$n = 25$$, sample mean $$\bar{x} = 47$$, and known $$\sigma = 5. $$What is the test statistic?

Accepted Answer

$$z = \frac{47 - 50}{5/\sqrt{25}} = -3.0$$

Question 4

A city claims the average commute time is 30 minutes. A sample of 40 commuters has a mean of 28 minutes and a standard deviation of 6 minutes. Test the claim at $$\alpha = 0.05. $$What is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is sufficient evidence to conclude the mean commute time is different from 30 minutes.

Question 5

In a two-tailed test, the test statistic is $$z = -2.05. $$What is the P-value?

Accepted Answer

$$0.0404$$

Question 6

A sample of 54 employees has a mean weight of 183.9 lb. The population standard deviation is 121.2 lb. Test the claim that the population mean is less than 200 lb at $$\alpha = 0.10. $$What is the test statistic?

Accepted Answer

$$z = \frac{183.9 - 200}{121.2/\sqrt{54}} = -0.98$$

Question 7

A scientist claims that the mean temperature in a city is 22°C. A sample of 60 days has a mean of 20°C and a standard deviation of 1.5°C. Test the claim at $$\alpha = 0.05. $$What is the P-value?

Accepted Answer

$$0.0002$$

Question 8

A sobriety test is given to 20 sober subjects, yielding a mean score of 41.0 and a standard deviation of 3.7. Test the claim that the true mean is 35.0 at $$\alpha = 0.01. $$What is the test statistic?

Accepted Answer

$$t = \frac{41.0 - 35.0}{3.7/\sqrt{20}} = 7.252$$

Question 9

A poll claims 53% of Americans support the incumbent president. In a sample of 100, 45% support the president. Test the claim at $$\alpha = 0.10. $$What is the P-value?

Accepted Answer

$$0.0548$$

Question 10

A sample of 9 scores has $$\bar{x} = 3.17$$ and $$s = 0.57. $$Test $$H_0$$: \mu = 2.85$$ versus H_1$: \mu \u003e 2.85 at$$ $$\alpha = 0.01. $$What is the test statistic?

Accepted Answer

$$t = \frac{3.17 - 2.85}{0.57/\sqrt{9}} = 1.68$$

Question 11

A town claims the mean annual salary is $$30,000. A sample of 17 adults has a mean of 22$$,298 and a standard deviation of $$14,200. Test the claim at $$\alpha = 0.05$. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that $$\mu = 30,000.$$

Question 12

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

Accepted Answer

The probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.

Question 13

A right-tailed test yields a test statistic $$z = 0.52. $$What is the correct P-value and conclusion at $$\alpha = 0.05$$?

Accepted Answer

$$0.3015$$; fail to reject the null hypothesis

Question 14

In a two-tailed test, the test statistic is $$z = -1.63. $$What is the correct P-value and conclusion at $$\alpha = 0.05$$?

Accepted Answer

$$0.1032$$; fail to reject the null hypothesis

Question 15

A left-tailed test with $$z = -1.93 is $$performed. What is the P-value and conclusion at $$\alpha = 0.05$$?

Accepted Answer

$$0.0268$$; reject the null hypothesis

Question 16

A two-tailed test is performed with $$H_1$$: p 
eq 3/5$$ and z = 0.78$. What is the P-value and conclusion at $$\alpha = 0.05$$?

Accepted Answer

$$0.4354$$; fail to reject the null hypothesis

Question 17

Which of the following is NOT a correct step in hypothesis testing?

Accepted Answer

Accept the null hypothesis if the P-value is greater than the significance level.

Question 18

A scientist claims that fewer than 14 in ten thousand male fireflies are unable to produce light due to a genetic mutation. The null hypothesis is rejected. What is the correct nontechnical conclusion?

Accepted Answer

There is sufficient evidence to support the claim that the true proportion is less than 14 in ten thousand.

Step-by-Step Guidance for Hypothesis Testing and P-Value Interpretation (Chapter 8)

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