Q: A researcher wants to test if the mean cholesterol level in a population is different from 200 mg/dL. Which of the following is the correct set of hypotheses for a two-tailed test?

$$H_0$$: \mu = 200,\ $$H_1$$: \mu \neq 200$$

Question 1

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

Accepted Answer

Rejecting a true null hypothesis

Question 2

A pharmaceutical company claims that at least 90% of patients recover after using their new drug. In a clinical trial, 180 out of 200 patients recovered. Test the company's claim at $$\alpha = 0.05. $$What is the correct null and alternative hypothesis for this scenario?

Accepted Answer

$$H_0$$: p = 0.90,\ $$H_1$$: p \u003e 0.90$$

Question 3

In hypothesis testing, what does the level of significance $$\alpha$$ represent?

Accepted Answer

The probability of making a Type I error

Question 4

A researcher wants to test if the mean cholesterol level in a population is different from 200 mg/dL. Which of the following is the correct set of hypotheses for a two-tailed test?

Accepted Answer

$$H_0$$: \mu = 200,\ $$H_1$$: \mu 
eq 200$$

Question 5

Suppose you are testing $$H_0$$: p = 0.5$$ vs H_1$: p \u003e 0.5 at$$ $$\alpha = 0.05$$ using a sample of $$n = 100$$ with $$p̂ = 0.56. $$What is the value of the test statistic?

Accepted Answer

$$z = \dfrac{0.56 - 0.5}{\sqrt{0.5(1-0.5)/100}} = 1.6$$

Question 6

Which of the following statements about p-values is correct?

Accepted Answer

A p-value less than $$\alpha$$ means we reject the null hypothesis.

Question 7

A sample of 25 students has a mean test score of 78 and a standard deviation of 10. The population mean is hypothesized to be 75. What is the value of the test statistic for testing $$H_0$$: \mu = 75$$?

Accepted Answer

$$t = \dfrac{78 - 75}{10/\sqrt{25}} = 1.5$$

Question 8

Which distribution is used for hypothesis testing about a population mean when the population standard deviation is unknown and the sample size is small?

Accepted Answer

t-distribution

Question 9

A manufacturer claims that the standard deviation of the weight of their cereal boxes is 2 grams. A sample of 15 boxes has a sample standard deviation of 2.5 grams. Which test statistic should be used to test the claim about the population standard deviation?

Accepted Answer

$$\$$chi^2$$ = \dfrac{(n-1)s^2$}{\$$sigma_0$$^2}$$

Question 10

Which of the following best describes the difference between statistical significance and practical significance?

Accepted Answer

Statistical significance means the result is unlikely to have occurred by chance, while practical significance means the result is important in real life.

Question 11

A left-tailed hypothesis test is being conducted at $$\alpha = 0.05. $$The calculated test statistic is $$z = -2.1. $$What is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 12

Which of the following is NOT a possible outcome of a hypothesis test?

Accepted Answer

Accepting the alternative hypothesis as true

Question 13

A sample of 40 batteries has a mean life of 520 hours with a standard deviation of 30 hours. The manufacturer claims the mean life is 500 hours. What is the value of the test statistic for $$H_0$$: \mu = 500$$?

Accepted Answer

$$t = \dfrac{520 - 500}{30/\sqrt{40}} = 4.22$$

Question 14

If the p-value for a hypothesis test is 0.08 and $$\alpha = 0.05$$, what should you conclude?

Accepted Answer

Fail to reject the null hypothesis.

Question 15

Which of the following scenarios would require a right-tailed test?

Accepted Answer

Testing if the proportion is greater than a specified value

Question 16

A hospital administrator wants to know if the proportion of patients who recover from a new treatment is different from 0.8. In a sample of 150 patients, 126 recover. What is the value of the test statistic for $$H_0$$: p = 0.8$$?

Accepted Answer

$$z = \dfrac{0.84 - 0.8}{\sqrt{0.8(1-0.8)/150}} = 1.55$$

Question 17

Which of the following is a correct interpretation of a 95% confidence interval for a population proportion?

Accepted Answer

If we repeated the sampling many times, about 95% of the intervals would contain the true population proportion.

Question 18

Which of the following is the correct formula for the test statistic when testing a hypothesis about a population mean with unknown standard deviation?

Accepted Answer

$$t = \dfrac{\bar{x} - \mu_0$}{s/\sqrt{n}}$$

Question 19

A company wants to test if the variance of the weights of their product is greater than 4.0. A sample of 12 products has a sample variance of 6.0. What is the value of the test statistic for $$H_0$$: \$$sigma^2 = 4.0$?

Accepted Answer

$$\$$chi^2$$ = \dfrac{(12-1)	imes6.0}{4.0} = 16.5$$

Hypothesis Testing: Concepts, Procedures, and Applications

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