Question 1

Which of the following best describes the purpose of hypothesis testing in statistics?

Accepted Answer

To determine whether there is enough evidence in a sample to infer that a certain condition holds for the entire population.

Question 2

A researcher claims that the mean time to complete a marathon is 4.5 hours. A random sample of 36 runners has a mean time of 4.3 hours with a known population standard deviation of 0.6 hours. At a 5% significance level, what is the null hypothesis ($$H_0) $$for this test?

Accepted Answer

$$H_0$$: \mu = 4.5$$

Question 3

Given a left-tailed z-test with a test statistic $$z = -2.05$$, and a significance level $$\alpha = 0.05$$, what is the correct decision rule using the P-value approach?

Accepted Answer

Reject $$H_0 if P-$$value $$\u003c \alpha$$

Question 4

A sample of 25 homes has a mean indoor winter temperature of 68°F. The population standard deviation is known to be 2°F. The hypothesized population mean is 70°F. Calculate the standardized test statistic $$z.$$

Accepted Answer

$$z = \frac{68 - 70}{2/\sqrt{25}} = -5$$

Question 5

Which of the following statements is true regarding the rejection region in hypothesis testing?

Accepted Answer

If the test statistic falls in the rejection region, you reject the null hypothesis.

Question 6

For a two-tailed test with $$\alpha = 0.05$$, what are the critical values for the standard normal distribution?

Accepted Answer

$$z = \pm 1.96$$

Question 7

A company claims its average delivery time is less than 2 days. A sample of 40 deliveries has a mean of 1.8 days and a known population standard deviation of 0.5 days. What is the alternative hypothesis ($$H_a) $$for this test?

Accepted Answer

$$H_a: \mu \u003c 2$$

Question 8

If the P-value for a hypothesis test is 0.012 and the significance level is $$\alpha = 0.01$$, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis.

Question 9

In a right-tailed test, the area to the right of the test statistic is 0.045. If $$\alpha = 0.05$$, what is the P-value and what decision should be made?

Accepted Answer

P-value = 0.045; reject the null hypothesis.

Question 10

A sample of 1000 parents reports a mean annual cost of raising a child as $$17,072, with a population standard deviation of 2$$,850. The hypothesized mean is $$17,250. $$Calculate the z-test statistic.

Accepted Answer

$$z = \frac{17,072 - 17,250}{2,850/\sqrt{1000}} \approx -2.10$$

Question 11

Which of the following is NOT an assumption for using the z-test for a mean when $$\sigma is $$known?

Accepted Answer

The population standard deviation is unknown.

Question 12

A pit crew claims its mean pit stop time is less than 13 seconds. A sample of 32 pit stops has a mean of 12.9 seconds and a population standard deviation of 0.19 seconds. What is the correct standardized test statistic?

Accepted Answer

$$z = \frac{12.9 - 13}{0.19/\sqrt{32}} \approx -2.98$$

Question 13

If a two-tailed test has a significance level of $$\alpha = 0.10$$, what is the area in each tail of the standard normal distribution?

Accepted Answer

$$0.05$$

Question 14

Which of the following best explains why a sample mean may differ from the population mean even if the null hypothesis is true?

Accepted Answer

Sampling error

Question 15

A left-tailed test has a critical value of $$z = -2.33. If $$the calculated test statistic is $$z = -2.50$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 16

Which of the following is the correct formula for the standard error of the mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$\frac{\sigma}{\sqrt{n}}$$

Hypothesis Testing with One Sample: Z-Test for the Mean (σ Known)

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