Q: A school claims that exactly 61% of its students participate in extracurricular activities. Which is the correct way to state the null and alternative hypotheses?

$$H_0$$: p = 0.61$$; H_a$$: p \neq 0.61$$

Question 1

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

Accepted Answer

A statement about a population parameter that contains an equality, such as $$\mu = k.$$

Question 2

A pharmaceutical company claims that their new drug reduces average recovery time to less than 10 days. Which is the correct way to state the null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu \geq 10$$; H_a$$: \mu \u003c 10$$

Question 3

Which of the following scenarios describes a Type I error?

Accepted Answer

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

Question 4

A researcher tests whether the mean cholesterol level in a population is different from 200 mg/dL. Which type of test should be used?

Accepted Answer

A two-tailed test

Question 5

If the significance level $$\alpha is $$set at 0.05 and the p-value for a hypothesis test is 0.03, what is the correct decision?

Accepted Answer

Reject the null hypothesis

Question 6

Which formula is used to calculate the standardized test statistic (z-score) for a sample mean when the population standard deviation is known?

Accepted Answer

$$z = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}}$$

Question 7

A hospital claims that the average wait time in their emergency room is at most 30 minutes. A sample of 40 patients has a mean wait time of 34 minutes with a known population standard deviation of 8 minutes. Test the hospital's claim at $$\alpha = 0.05. $$What is the correct standardized test statistic?

Accepted Answer

$$z = \frac{34 - 30}{8 / \sqrt{40}} = 3.16$$

Question 8

Which of the following best describes the power of a statistical test?

Accepted Answer

The probability of correctly rejecting $$H_0$$ when $$H_0 is $$false.

Question 9

A school claims that exactly 61% of its students participate in extracurricular activities. Which is the correct way to state the null and alternative hypotheses?

Accepted Answer

$$H_0$$: p = 0.61$$; H_a$$: p 
eq 0.61$$

Question 10

Which of the following is NOT an assumption required for using the z-test for a sample mean?

Accepted Answer

The population mean is unknown.

Question 11

A Type II error occurs when:

Accepted Answer

The null hypothesis is not rejected when it is false.

Question 12

A company advertises that the mean lifespan of its furnaces is more than 18 years. Which is the correct direction for the hypothesis test?

Accepted Answer

Right-tailed test

Question 13

If you obtain a p-value of 0.0129 for a left-tailed test and your significance level is $$\alpha = 0.01$$, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis

Question 14

Which of the following statements about the level of significance ($$\alpha) is $$TRUE?

Accepted Answer

It is the maximum probability of making a Type I error.

Question 15

A Toyota Prius is advertised to have a mean gas mileage of 50 mpg. A sample of 30 cars has a mean of 47 mpg and a population standard deviation of 5.5 mpg. What is the z-score for this sample mean?

Accepted Answer

$$z = \frac{47 - 50}{5.5 / \sqrt{30}} = -2.99$$

Question 16

Which of the following best describes a two-tailed hypothesis test?

Accepted Answer

The alternative hypothesis contains a not-equal-to symbol.

Question 17

In the context of hypothesis testing, what does the p-value represent?

Accepted Answer

The probability of obtaining a sample statistic as extreme or more extreme than the observed value, assuming $$H_0 is $$true.

Question 18

A meat inspector tests whether the proportion of contaminated ground beef exceeds the USDA limit of 7.5%. Which is the correct null and alternative hypothesis?

Accepted Answer

$$H_0$$: p \leq 0.075$$; H_a$$: p \u003e 0.075$$

Hypothesis Testing: Concepts, Errors, and z-Test for the Mean

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