Question 1

Which of the following best describes the null hypothesis ($$H_0) in $$hypothesis testing?

Accepted Answer

A statement about the population parameter that is assumed to be true unless evidence suggests otherwise.

Question 2

A tire company claims its tires last at least 60,000 miles on average. Which is the correct way to state the null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu \geq 60,000$$ 
H_A$$: \mu \u003c 60,000$$

Question 3

Which of the following significance levels ($$\alpha) $$corresponds to a 95% confidence level?

Accepted Answer

$$\alpha = 0.05$$

Question 4

A company wants to test if the mean fill of cereal boxes is different from 16 ounces. Which type of test should be used?

Accepted Answer

A two-tailed test

Question 5

If the population standard deviation ($$\sigma) is $$unknown and the sample size is small ($$n \u003c 30$$), which test statistic should be used?

Accepted Answer

t-test

Question 6

A sample of 64 homes has a mean construction time of 24 days. The population mean is 25 days, $$\sigma = 3$$, and $$\alpha = 0.10. $$What is the value of the test statistic?

Accepted Answer

$$Z = \frac{24-25}{3/\sqrt{64}} = -2.67$$

Question 7

What is a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 8

If the p-value is 0.016 and $$\alpha = 0.05$$, what is the correct decision?

Accepted Answer

Reject $$H_0$$

Question 9

Which of the following is the correct formula for the test statistic when the population standard deviation is known?

Accepted Answer

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

Question 10

A production manager samples 16 cartons, finds $$\bar{x} = 64.2$$, $$s = 0.72$$, $$\mu_0$ = 64$$, and $$\alpha = 0.05. $$What is the test statistic?

Accepted Answer

$$t = \frac{64.2-64}{0.72/\sqrt{16}} = 1.11$$

Question 11

In a two-tailed test with $$\alpha = 0.05$$, what are the critical values for the Z-test?

Accepted Answer

$$-1.96$$ and $$1.96$$

Question 12

Which of the following best describes the p-value?

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 city mayor claims the mean time spent in parking spaces exceeds 33 minutes. What is the correct alternative hypothesis?

Accepted Answer

$$H_A: \mu \u003e 33$$

Question 14

If the test statistic falls in the rejection region, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 15

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

Accepted Answer

Calculate the sample variance

Question 16

A department claims average rainfall is at least 23 inches. Which is the correct null hypothesis?

Accepted Answer

$$H_0$$: \mu \geq 23$$

Question 17

If you double the p-value in a two-tailed test, what does this account for?

Accepted Answer

Both tails of the distribution

Question 18

Which of the following is true about the alternative hypothesis ($$H_A$$)?

Accepted Answer

It is accepted if the sample data provide sufficient evidence that the null hypothesis is false.

Question 19

A test statistic is calculated as $$Z = 2.15$$ with $$\alpha = 0.05 ($$right-tailed test). What is the p-value and what decision should be made?

Accepted Answer

p-value = 0.016, reject $$H_0$$

Hypothesis Testing for a Population Mean: Structured Study Notes

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