Question

A politician claims that people don't really understand the stem cell issue, and their responses to such questions are random responses equivalent to a coin toss. Exclude the 118 subjects who said they were unsure and use a 0.10 significance level to test the claim that the proportion of subjects who respond in favor is equal to 0.5. What does the result suggest about the politician's claim?

Identify the null and alternative hypotheses for this test:
A. Null Hypothesis (H0): p = 0.5, Alternative Hypothesis (H1): p ≠ 0.5
B. Null Hypothesis (H0): p = 0.5, Alternative Hypothesis (H1): p > 0.5
C. Null Hypothesis (H0): p ≤ 0.5, Alternative Hypothesis (H1): p < 0.5
D. Null Hypothesis (H0): p = 0.5, Alternative Hypothesis (H1): p ≠ 0.5

Answer 1

The correct hypotheses are the null hypothesis that the proportion is p = 0.5 and the alternative hypothesis that the proportion is p ≠ 0.5. A high p-value suggests that we would not reject the null hypothesis, indicating that the data does not strongly dispute the claim of random responses.

Step-by-step explanation:

The correct identification of the null and alternative hypotheses for the given stem cell study is Option A, where:

• Null Hypothesis (H0): p = 0.5
• Alternative Hypothesis (H1): p ≠ 0.5

This is because the claim being tested is whether the proportion of subjects responding in favor differs from 0.5 (the value one would expect from random responses like a coin toss).

The p-value is a probability that measures the evidence against the null hypothesis. In this context, if the proportion were really 0.5, the probability of observing a sample proportion of 0.53 or more, or 0.47 or less, is 0.5485, or 54.85%. Since this p-value is high and would be greater than the significance level of 0.10, we would not reject the null hypothesis, suggesting that the data does not provide strong evidence against the claim that responses are random. However, to make a definitive conclusion, actual sample proportions and the exact calculated p-value from the study data would be needed.