Question 1

A researcher wants to estimate the proportion of shoplifters among customers entering a store. In a random sample of 120 customers, 5 are detected as shoplifters. Construct a 95% confidence interval for the proportion of shoplifters, and interpret the result.

Accepted Answer

$$0.013 \u003c p \u003c 0.070$$; We are 95% confident that the true proportion of shoplifters is between 1.3% and 7.0%.

Question 2

A Type I error occurs when:

Accepted Answer

We reject the null hypothesis when it is actually true.

Question 3

A psychologist claims that 40% of patients in his practice have a psychosomatic disorder. To test if this proportion has decreased, a random sample of 80 patients is taken, and 25 are found to have the disorder. What is the value of the test statistic for testing $$H_0$$: p = 0.4$$ vs H_a$$: p \u003c 0.4$$?

Accepted Answer

$$z = -1.25$$

Question 4

A company claims that its new juice bottling machine fills bottles with an average of 20 ounces. A consumer group tests 12 bottles and finds a sample mean of 19.8 ounces with a standard deviation of 0.3 ounces. What is the 95% confidence interval for the true mean fill?

Accepted Answer

$$19.59 \u003c \mu \u003c 20.01$$

Question 5

Which of the following best describes the consequence of a Type II error in the context of a medical test for a disease?

Accepted Answer

Failing to detect the disease when it is actually present.

Question 6

A new reading program is tested on a class of 20 children. Their reading scores before and after the program are compared. Which statistical test is most appropriate?

Accepted Answer

Paired t-test

Question 7

A frozen orange juice company claims that 70% of all orange juice drinkers prefer its product. A random sample of 100 drinkers finds that 62 prefer the company's brand. What is the p-value for testing $$H_0$$: p = 0.7$$ vs H_a$$: p 
eq 0.7$$?

Accepted Answer

$$p = 0.048$$

Question 8

A sociologist wants to test if annual income is related to the commission of crimes. She collects a random sample of severity of penalty, all of whom live in the same city and none of whom has a criminal record, and records their annual incomes. What is the correct method of analysis?

Accepted Answer

Independent samples t-test

Question 9

A clinical trial tests whether a new drug reduces blood pressure. The mean reduction in blood pressure for the treatment group is 8 mmHg with a standard deviation of 4 mmHg, and for the control group is 5 mmHg with a standard deviation of 3 mmHg. Each group has 25 participants. What is the value of the test statistic for $$H_0$$: \$$mu_1$$ = \$$mu_2$$?

Accepted Answer

$$t = 2.83$$

Question 10

A manufacturer develops a new pain reliever and wants to test if it is more effective than the current leading brand. Twenty patients are randomly assigned to each treatment. What is the most appropriate hypothesis test?

Accepted Answer

Two-sample t-test for independent means

Question 11

A study finds that 80% of cats show signs of shock after exposure to a certain drug. If we take many random samples of 50 cats, about 8 out of 10 of them would produce this result. What is the 95% confidence interval for the proportion of cats showing shock in a sample of 50?

Accepted Answer

$$0.68 \u003c p \u003c 0.92$$

Question 12

A new weight-reducing diet is being tested. The mean weight loss in a random sample of 15 subjects is 8.2 pounds with a standard deviation of 2.5 pounds. What is the 95% confidence interval for the mean weight loss?

Accepted Answer

$$6.93 \u003c \mu \u003c 9.47$$

Question 13

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

Accepted Answer

A p-value is the probability of obtaining a result as extreme as, or more extreme than, the observed result, assuming the null hypothesis is true.

Question 14

A hospital administrator claims that the average ER wait time is 40 minutes. A random sample of 60 patients has a mean wait time of 38 minutes and a standard deviation of 11 minutes. What is the value of the test statistic for $$H_0$$: \mu = 40$$?

Accepted Answer

$$z = -1.38$$

Question 15

A Type II error in the context of a consumer product test (e.g., juice bottle fill) would mean:

Accepted Answer

Failing to detect that the bottles are underfilled when they actually are.

Question 16

A college counseling center wants to test if an assertiveness training course increases students' self-esteem. Students are tested before and after the course. What is the correct statistical method?

Accepted Answer

Paired samples t-test

Question 17

A new band for children with braces is being tested for comfort. A sample of 30 children rates the new band and the old band. The mean difference in comfort scores is 1.2 with a standard deviation of 2.0. What is the value of the test statistic for $$H_0$$: \mu_d = 0$$?

Accepted Answer

$$t = 3.29$$

Question 18

A study finds that the mean score of heroin addicts is less than that of the general population. The test is conducted at a 5% level of significance. What is the correct interpretation if the p-value is 0.03?

Accepted Answer

There is sufficient evidence to conclude that the mean score of heroin addicts is less than that of the general population.

Practice Problems and Concepts in Hypothesis Testing and Confidence Intervals

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드