Part 2 of 5
Points: 0 of 1
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, 481 were in favor, 397 were opposed, and 124 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 124 subjects who said that they were unsure, and use a 0.01 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.
\[
\begin{array}{l}
H_{0}: p \neq 0.5 \\
H_{1}: p=0.5
\end{array}
\]
B. $\mathrm{H}_{0} \cdot \mathrm{p}=0.5$
\[
H_{1}: p> 0.5
\]
\[
\begin{array}{l}
H_{0}: p=0.5 \\
H_{1}: p< 0.5 \\
H_{0}: p=0.5 \\
H_{1}: p \neq 0.5
\end{array}
\]
Identify the test statistic for this hypothesis test
The test statistic for this hypothesis test is $\square$
(Round to two decimal places as needed)
Clear all
Answer
Final Answer: The null and alternative hypotheses for this test are: \[\begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p \neq 0.5 \end{array}\] The test statistic for this hypothesis test is \(\boxed{2.83}\).
Step 1 ：The null hypothesis is a statement of no effect or status quo. In this case, it would be that the proportion of subjects who respond in favor is equal to 0.5. The alternative hypothesis is what we are testing against the null hypothesis. In this case, it would be that the proportion of subjects who respond in favor is not equal to 0.5. So, the null and alternative hypotheses for this test are: \[\begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p \neq 0.5 \end{array}\]
Step 2 ：The test statistic can be calculated using the formula for a one-sample z-test for proportions, which is \((p_{hat} - p_0) / \sqrt{(p_0 * (1 - p_0)) / n}\), where \(p_{hat}\) is the sample proportion, \(p_0\) is the hypothesized population proportion, and n is the sample size.
Step 3 ：Given that the number of adults in favor is 481, the number of adults opposed is 397, and the total number of adults is 878, we can calculate the sample proportion \(p_{hat}\) as 0.5478359908883826.
Step 4 ：Substituting these values into the formula, we get the test statistic as approximately 2.83.
Step 5 ：Final Answer: The null and alternative hypotheses for this test are: \[\begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p \neq 0.5 \end{array}\] The test statistic for this hypothesis test is \(\boxed{2.83}\).
