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.)
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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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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