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

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Statistics

Assume that adults were randomly selected for a poll. They wereasked if they​ \"favor or oppose using federal tax dollars to fundmedical research using stem cells obtained from human​ embryos.\" Ofthose​ polled,

484484

were in​ favor,

395395

were​ opposed, and

118118

were unsure. A politician claims that people​ don't reallyunderstand the stem cell issue and their responses to suchquestions are random responses equivalent to a coin toss. Excludethe

118118

subjects who said that they were​ unsure, and use a

0.010.01

significance level to test the claim that the proportion ofsubjects who respond in favor is equal to

0.50.5.

What does the result suggest about the​ politician's claim?

Answer & Explanation Solved by verified expert
4.2 Ratings (478 Votes)

null Hypothesis:               Ho:   p = 0.500
alternate Hypothesis:    Ha: p ≠ 0.500
for 0.01 level with two tailed test , critical z= 2.576
Decision rule :   reject Ho if absolute value of test statistic |z|>2.576
sample success x   = 484
sample size          n    = 879
std error   se =√(p*(1-p)/n) = 0.0169
sample proportion p̂ = x/n= 0.5506
test stat z =(p̂-p)/√(p(1-p)/n)= 3.00
p value                          = 0.003
since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to reject the politician's claim
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