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,

484484

were in​ favor,

395395

were​ opposed, and

118118

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

118118

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

0.010.01

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

0.50.5.

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

Answer 1

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