Questions: Assume that adults were randomly selected for a poll. They were asked if they "favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos." Of those polled, 489 were in favor, 396 were opposed, and 122 were unsure. 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 122 subjects who said that 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. Choose the correct answer below. A. H0: p ≠ 0.5 H1: p=0.5 B. H0: p=0.5 H1: p>0.5 C. H0: p=0.5 H1: p ≠ 0.5 D. H0: p=0.5 H1: p<0.5 Identify the test statistic for this hypothesis test. - The test statistic for this hypothesis test is . (Round to two decimal places as needed.)

Assume that adults were randomly selected for a poll. They were asked if they "favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos." Of those polled, 489 were in favor, 396 were opposed, and 122 were unsure. 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 122 subjects who said that 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. Choose the correct answer below. A. H0: p ≠ 0.5 H1: p=0.5 B. H0: p=0.5 H1: p>0.5 C. H0: p=0.5 H1: p ≠ 0.5 D. H0: p=0.5 H1: p<0.5 Identify the test statistic for this hypothesis test. - The test statistic for this hypothesis test is . (Round to two decimal places as needed.)
Transcript text: Assume that adults were randomly selected for a poll. They were asked if they "favor or oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos." Of those polled, 489 were in favor, 396 were opposed, and 122 were unsure. 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 122 subjects who said that 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. Choose the correct answer below. A. $H_{0}: p \neq 0.5$ $H_{1}: p=0.5$ B. $H_{0}: p=0.5$ $H_{1}: p>0.5$ C. $H_{0}: p=0.5$ $H_{1}: p \neq 0.5$ D. $H_{0}: p=0.5$ $H_{1}: p<0.5$ Identify the test statistic for this hypothesis test. - The test statistic for this hypothesis test is $\square$ $\square$. (Round to two decimal places as needed.) View an example Get more help Clear all Check answer
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Solution

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Solution Steps

Step 1: Define the Hypotheses

We are testing the claim regarding the proportion of subjects who favor using federal tax dollars to fund medical research using stem cells obtained from human embryos. The null and alternative hypotheses are defined as follows:

  • Null Hypothesis: \( H_0: p = 0.5 \)
  • Alternative Hypothesis: \( H_1: p \neq 0.5 \)
Step 2: Calculate the Test Statistic

The test statistic for the proportion is calculated using the formula:

\[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \]

Substituting the values:

  • Sample proportion \( \hat{p} = \frac{489}{489 + 396} = 0.5523 \)
  • Hypothesized proportion \( p_0 = 0.5 \)
  • Sample size \( n = 489 + 396 = 885 \)

The calculated test statistic is:

\[ Z = 3.1262 \]

Step 3: Determine the P-value

The P-value associated with the test statistic \( Z = 3.1262 \) is found to be:

\[ \text{P-value} = 0.0018 \]

Step 4: Identify the Critical Region

For a significance level of \( \alpha = 0.10 \) in a two-tailed test, the critical region is defined as:

\[ Z < -1.6449 \quad \text{or} \quad Z > 1.6449 \]

Step 5: Make a Decision

Since the calculated test statistic \( Z = 3.1262 \) falls into the critical region (i.e., \( Z > 1.6449 \)), we reject the null hypothesis.

Step 6: Conclusion

The results suggest that there is sufficient evidence to conclude that the proportion of subjects who favor the use of federal tax dollars for stem cell research is not equal to \( 0.5 \). This indicates that the politician's claim that people's responses are random is not supported by the data.

Final Answer

The answer is \( \boxed{H_0: p = 0.5, H_1: p \neq 0.5} \) and the conclusion is to reject the null hypothesis.

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