Question

A researcher wanted to determine the effectiveness of a new cream in the treatment of warts. She identified 145 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 alpha equals 0.05 level of significance. Treatment ATreatment B Success Failure Success 61 11 Failure 21 52(a) What type of test should be used? A. A hypothesis test regarding the difference of two means using a matched-pairs design B. A hypothesis test regarding the difference between two population proportions from dependent samples C. A hypothesis test regarding two population standard deviations D. A hypothesis test regarding the difference between two population proportions from independent samples (b) Determine the null and alternative hypotheses. A. H0 : p1 = p2, H1 : p1 >p2B. H0 : p1 < p2, H1 : p1 >p2C. H0 : p1 = p2, H1 : p1

Answer 1

The test to use for comparing the effectiveness of two treatments for warts is a hypothesis test for the difference between two population proportions from dependent samples. The null hypothesis states the proportions are equal (H0: p1 = p2), while the alternative hypothesis suggests they are not equal (H1: p1 ≠ p2).

Step-by-step explanation:

The correct answer to the student's question is:

• (a) B. A hypothesis test regarding the difference between two population proportions from dependent samples.
• (b) The null hypothesis (H0) is that the proportion of successes with cream A (p1) is equal to the proportion of successes with cream B (p2): H0: p1 = p2. The alternative hypothesis (H1) is that the proportions are not equal, indicating that there is a difference in the effectiveness of the two creams: H1: p1 ≠ p2.

Since each individual received both treatments and we compare the success between two treatments on the same subjects, we should use a paired samples design (dependent samples).

Answer 2

a. Option D

b. H₀ : p₁ = p₂, H₁: p1 ≠ p₂

Step-by-step explanation:

a. A hypothesis test regarding the difference between two population proportions from independent samples. This type of test is used to compare the proportions of two populations. This test is usually appropriate under the conditions that:

The sampling method for each population is simple random sampling.

The samples are independent.

Each sample includes at least 10 successes and 10 failures.

Each population is at least 20 times as big as its sample.

b. Null hypothesis: H₀ : p₁ = p₂

Alternative hypothesis: H₁ : p₁ ≠ p₂