Q: A company claims that the average lifetime of its light bulbs is at least 8,000 hours. A random sample of 36 bulbs has a mean lifetime of 7,850 hours with a known population standard deviation of 300 hours. At a significance level of $$\alpha = 0.05$$, which of the following is the correct test statistic and conclusion for this upper-tailed test?

$$z = \frac{7850 - 8000}{300/\sqrt{36}} = -3.00$$, \text{Reject } $$H_0$

Q: A researcher wants to test if the average time spent on a website is different from 5 minutes. A sample of 49 users has a mean of 5.4 minutes and a known population standard deviation of 1.4 minutes. What is the correct null and alternative hypothesis for this scenario?

$$H_0$$: \mu = 5$$, H_1$: \mu \neq 5$$

Q: A sample of 100 college students is used to test if the proportion who own a laptop is different from 0.75. If 82 students own a laptop, what is the value of the test statistic for the proportion?

$$z = \frac{0.82 - 0.75}{\sqrt{0.75 \times 0.25 / 100}}$$

Question 1

A company claims that the average lifetime of its light bulbs is at least 8,000 hours. A random sample of 36 bulbs has a mean lifetime of 7,850 hours with a known population standard deviation of 300 hours. At a significance level of $$\alpha = 0.05$$, which of the following is the correct test statistic and conclusion for this upper-tailed test?

Accepted Answer

$$z = \frac{7850 - 8000}{300/\sqrt{36}} = -3.00$$, 	ext{Reject } $$H_0$

Question 2

Which of the following statements best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting $$H_0$$ when $$H_0 is $$true

Question 3

A researcher wants to test if the average time spent on a website is different from 5 minutes. A sample of 49 users has a mean of 5.4 minutes and a known population standard deviation of 1.4 minutes. What is the correct null and alternative hypothesis for this scenario?

Accepted Answer

$$H_0$$: \mu = 5$$, H_1$: \mu 
eq 5$$

Question 4

Suppose the population standard deviation is unknown. A sample of 16 students has a mean test score of 78 and a sample standard deviation of 8. The test is to determine if the average score is greater than 75 at $$\alpha = 0.05. $$What is the appropriate test statistic?

Accepted Answer

$$t = \frac{78 - 75}{8/4} = 1.5$$

Question 5

A hospital administrator claims that the average wait time in the emergency room is less than 30 minutes. A random sample of 25 patients has a mean wait time of 28 minutes and a sample standard deviation of 6 minutes. What is the correct rejection region for a left-tailed t-test at $$\alpha = 0.05$$?

Accepted Answer

$$t_{calc} \u003c -t_{\alpha}$$

Question 6

Which formula is used to calculate the test statistic for a one-sample z-test for the mean when $$\sigma is $$known?

Accepted Answer

$$z = \frac{\bar{x} - \mu_0$}{\sigma/\sqrt{n}}$$

Question 7

A survey claims that 60% of adults exercise regularly. In a sample of 200 adults, 130 say they exercise regularly. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{130}{200} = 0.65$$

Question 8

Which of the following conditions must be met to use the normal approximation for a hypothesis test about a population proportion?

Accepted Answer

$$np \geq 5$$ and $$n(1-p) \geq 5$$

Question 9

A two-tailed z-test is performed at $$\alpha = 0.05. $$The calculated test statistic is $$z = 2.2. $$What is the correct conclusion?

Accepted Answer

Reject $$H_0$$ because $$|z| \u003e z_{\alpha/2}$$

Question 10

If the significance level $$\alpha is $$decreased from 0.05 to 0.01, what is the effect on the probability of a Type II error ($$\beta$$), assuming the sample size remains the same?

Accepted Answer

$$\beta$$ increases

Question 11

A sample of 100 college students is used to test if the proportion who own a laptop is different from 0.75. If 82 students own a laptop, what is the value of the test statistic for the proportion?

Accepted Answer

$$z = \frac{0.82 - 0.75}{\sqrt{0.75 	imes 0.25 / 100}}$$

Question 12

Which of the following best describes the Central Limit Theorem as it applies to hypothesis testing?

Accepted Answer

The sampling distribution of the sample mean approaches normality as sample size increases, regardless of the population distribution

Question 13

A business wants to test if the average monthly sales are less than $$10,000. A sample of 20 months yields a mean of 9$$,500 and a sample standard deviation of $1,200. What is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: \mu \u003c 10,000$$

Question 14

In a left-tailed z-test, which of the following is the correct decision rule for rejecting the null hypothesis?

Accepted Answer

Reject $$H_0 if$$ $$z_{calc} \u003c -z_{\alpha}$$

Question 15

A sample of 30 batteries has a mean life of 510 hours and a known population standard deviation of 40 hours. The manufacturer claims the mean life is at least 500 hours. What is the p-value for the test statistic $$z = 1.37 in a $$right-tailed test?

Accepted Answer

$$p = 1 - P(Z \u003c 1.37)$$

Question 16

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

Accepted Answer

Calculate the sample variance

Hypothesis Testing: One-Sample Tests for Means and Proportions

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