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, 485 were in favor, 402 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 0.01 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?

The test statistic for this hypothesis test is_________

The? P-value for this hypothesis test is_________

Answer 1

we have 0.5 or 1/2 probability when tossing a coin.

So, population proportion is given equivalent to 0.5 (equivalent to a coin toss), so

Null hypothesis:

Alternate hypothesis:

It is a two tailed hypothesis because we want to determine whether the proportion of subjects who respond in favor is equal to 0.5 or not.

Sample proportion = (people who opposed)/(total people) = 485/(485+402) =485/887= 0.55 =

sample size is given as n = 485

we have to use the z statistic formula

z =

setting the values, we get

z =

so, test statistic for hypothesis is z = 2.20 (rounded to two decimals)

Now, using normal distribution table for the z value of 2.20 with two tails, we get the required p value

p value = 0.0278 which is more than 0.01

So, p value is insignificant at 0.01 level of significance and we can't reject the null hypothesis.

Thus, we can conclude that we don't have enough evidence to support the alternate hypothesis or we can say that we dont have enough evidence to reject that the proportion of subjects who respond in favor is equal to 0.5.