Assume that adults were randomly selected for a poll. They were asked if they \"

Question

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, 403 were opposed, and 125 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 125 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. Upper H 0 : pequals 0.5Upper H 1 : pgreater than 0.5 B. Upper H 0 : pnot equals 0.5Upper H 1 : pequals 0.5 C. Upper H 0 : pequals 0.5Upper H 1 : pnot equals 0.5 This is the correct answer. D. Upper H 0 : pequals 0.5Upper H 1 : pless than 0.5 Your answer is not correct. Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is . (Round to two decimal places as needed.)

Explanation / Answer

p = 481/(481+403) = .5441
p = .50

Ho: p = .50
Ha: p!= .50
alpha = .10

Correct answer therefore : C. Upper H 0 ?: pequals 0.5Upper H 1 ?: pnot equals 0.5

Test statistic:Z =
(p-p0)/sqrt(p0*p0'/n)
= (.5441-.5)/sqrt(.50*.50/884)
= 2.62

The test statistic for this test is Z = 2.62

For a test statistic of Z = 2.62, p-value is .044 and hence, much less than the critical region of .10. Therefore we reject null hypothesis ( that p0 = .50) and conclude that p is actually greater than .5

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