Q: A researcher wants to test whether the average time spent on a website is different from 56 seconds. Which of the following is the correct set of hypotheses for this test?

$$H_0$$: \mu = 56$$ and H_1$: \mu \neq 56$$

Question 1

A researcher wants to test whether the average time spent on a website is different from 56 seconds. Which of the following is the correct set of hypotheses for this test?

Accepted Answer

$$H_0$$: \mu = 56$$ and H_1$: \mu 
eq 56$$

Question 2

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

Accepted Answer

Rejecting the null hypothesis when it is true

Question 3

A company claims its new light bulb lasts more than 8,000 hours. You collect a sample and set up the following hypotheses: $$H_0$$: \mu \leq 8,000$$ hours, H_1$: \mu \u003e 8,000$$ hours. What type of test is this?

Accepted Answer

An upper-tail test

Question 4

Suppose you are testing $$H_0$$: \mu = 56$$ against H_1$: \mu 
eq 56$$ with $$\alpha = 0.05. $$What is the critical z-score for this two-tail test?

Accepted Answer

$$z_{\alpha/2} = 1.96$$

Question 5

Which formula should you use to calculate the test statistic when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$z_{\overline{x}} = \frac{\overline{x} - \mu_{H_0$}}{\sigma / \sqrt{n}}$$

Question 6

A sample of 36 bulbs has a mean life of 8,120 hours, $$\sigma = 500$$, and $$\mu_{H_0$} = 8,000. $$Calculate the z-test statistic.

Accepted Answer

$$z = \frac{8,120 - 8,000}{500 / \sqrt{36}} = 1.44$$

Question 7

If your calculated z-test statistic is 1.44 and the critical value for $$\alpha = 0.05 ($$one-tail) is 1.645, what is your decision?

Accepted Answer

Fail to reject $$H_0$$

Question 8

When the population standard deviation $$\sigma is $$unknown, which distribution should you use for hypothesis testing?

Accepted Answer

Student's t-distribution

Question 9

A sample of 12 self-serve checkout times has $$\overline{x} = 4.2$$ minutes, $$s = 1.42$$ minutes, and $$\mu_{H_0$} = 5$$ minutes. What is the t-test statistic?

Accepted Answer

$$t = \frac{4.2 - 5}{1.42 / \sqrt{12}} = -1.95$$

Question 10

Which of the following statements about $$\alpha$$ and $$\beta is $$correct?

Accepted Answer

Increasing $$\alpha$$ decreases $$\beta$$ for a fixed sample size

Question 11

In the context of FDA drug approval, what is a Type II error?

Accepted Answer

Not approving a beneficial drug

Question 12

Which formula is used to calculate the sample proportion in a hypothesis test for proportions?

Accepted Answer

$$\hat{p} = \frac{x}{n}$$

Question 13

A sample of 240 LinkedIn users contains 96 users aged 30–39. What is the sample proportion?

Accepted Answer

$$\hat{p} = \frac{96}{240} = 0.40$$

Question 14

Which formula is used to calculate the z-test statistic for a hypothesis test for a population proportion?

Accepted Answer

$$z_p = \frac{\hat{p} - p_0$}{\sqrt{\frac{p_0$ (1 - p_0$)}{n}}}$$

Question 15

If the p-value for a test is 0.0348 and $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject $$H_0$$

Question 16

Which of the following increases the power of a hypothesis test?

Accepted Answer

Increasing the sample size

Question 17

A Type II error is also known as:

Accepted Answer

Consumer's risk

Question 18

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

Accepted Answer

If the p-value is less than $$\alpha$$, reject $$H_0$$

Hypothesis Testing for a Single Population: Concepts, Procedures, and Applications

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