Use the following information to complete parts (a) through (e) below. A researcher wanted to determine the effectiveness of a new cream in the treatment of warts. She identified 136 individuals who had two warts. She applied cream A on one wart and cream B on the second wart. Test whether the proportion of successes with cream A is different from cream B at the a=0.01 level of significance. Treatment A Success 62 13 Failure Treatment B Success Failure 10 51 (a) What type of test should be used? O A. Ahypothesis test regarding the difference between two population proportions from independent samples O B. A hypothesis test regarding the difference of two means using a matched-pairs design OC. Ahypothesis test regarding two population standard deviations D. A hypothesis test regarding the difference between two population proportions from dependent samples (b) Determine the null and alternative hypotheses. Assume the warts treated with cream A are population 1 and the warts treated with cream B are population 2. Choose the correct answer below. O A. Ho: P1 =P2; H: P1> P2 O B. Ho: P1 =P2; H: P1 P2 (c) Calculate the test statistic. X = (Round to two decimal places as needed.)

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### Analysis of Warts Treatment Effectiveness Using Proportions

The following analysis investigates the effectiveness of two different creams, referred to as Cream A and Cream B, in the treatment of warts. The study involved 136 individuals, each with two warts. Cream A was applied to one wart and Cream B to the other wart on each individual. The goal is to determine if there is a significant difference in the proportion of successful treatments between Cream A and Cream B at the 0.01 level of significance. 

#### Data Summary

| Treatment | Success | Failure |
|-----------|---------|---------|
| Cream A   | 62      | 10      |
| Cream B   | 13      | 51      |

#### (a) Appropriate Statistical Test

Q: What type of test should be used?

- ○ A. A hypothesis test regarding the difference between two population proportions from independent samples
- ○ B. A hypothesis test regarding the difference of two means using a matched-pairs design
- ○ C. A hypothesis test regarding two population standard deviations
- ✔ D. A hypothesis test regarding the difference between two population proportions from dependent samples

**Answer:** The correct test is a hypothesis test regarding the difference between two population proportions from dependent samples.

#### (b) Null and Alternative Hypotheses

Q: Determine the null and alternative hypotheses. Assume the warts treated with Cream A are population 1 and the warts treated with Cream B are population 2. Choose the correct answer below.

- ○ A. \(H_0: p_1 = p_2\); \(H_1: p_1 > p_2\)
- ○ B. \(H_0: p_1 = p_2\); \(H_1: p_1 < p_2\)
- ✔ C. \(H_0: p_1 = p_2\); \(H_1: p_1 \neq p_2\)
- ○ D. \(H_0: p_1 \neq p_2\); \(H_1: p_1 > p_2\)

**Answer:** The null hypothesis (\(H_0\)) is that the proportions of successes for both treatments are equal (\(p_1 = p_2\)), while the alternative hypothesis (\(H_1\)) is that the proportions of successes for the treatments are not equal (\(p_
Transcribed Image Text:### Analysis of Warts Treatment Effectiveness Using Proportions The following analysis investigates the effectiveness of two different creams, referred to as Cream A and Cream B, in the treatment of warts. The study involved 136 individuals, each with two warts. Cream A was applied to one wart and Cream B to the other wart on each individual. The goal is to determine if there is a significant difference in the proportion of successful treatments between Cream A and Cream B at the 0.01 level of significance. #### Data Summary | Treatment | Success | Failure | |-----------|---------|---------| | Cream A | 62 | 10 | | Cream B | 13 | 51 | #### (a) Appropriate Statistical Test Q: What type of test should be used? - ○ A. A hypothesis test regarding the difference between two population proportions from independent samples - ○ B. A hypothesis test regarding the difference of two means using a matched-pairs design - ○ C. A hypothesis test regarding two population standard deviations - ✔ D. A hypothesis test regarding the difference between two population proportions from dependent samples **Answer:** The correct test is a hypothesis test regarding the difference between two population proportions from dependent samples. #### (b) Null and Alternative Hypotheses Q: Determine the null and alternative hypotheses. Assume the warts treated with Cream A are population 1 and the warts treated with Cream B are population 2. Choose the correct answer below. - ○ A. \(H_0: p_1 = p_2\); \(H_1: p_1 > p_2\) - ○ B. \(H_0: p_1 = p_2\); \(H_1: p_1 < p_2\) - ✔ C. \(H_0: p_1 = p_2\); \(H_1: p_1 \neq p_2\) - ○ D. \(H_0: p_1 \neq p_2\); \(H_1: p_1 > p_2\) **Answer:** The null hypothesis (\(H_0\)) is that the proportions of successes for both treatments are equal (\(p_1 = p_2\)), while the alternative hypothesis (\(H_1\)) is that the proportions of successes for the treatments are not equal (\(p_
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