Question

In: Statistics and Probability

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

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, 488 were in​ favor, 399 were​ opposed, and 121 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 121 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.

A.

Upper H 0​: p = 0.5

Upper H 1​: p < 0.5

B.

Upper H 0​: p = 0.5

Upper H 1​: p ≠ 0.5

C.

Upper H 0​: p ≠ 0.5

Upper H 1​: p = 0.5

D.

Upper H 0​: p = 0.5

Upper H 1​: p > 0.5

Identify the test statistic for this hypothesis test. ​(Round to two decimal places as​ needed.)

Identify the​ P-value for this hypothesis test. ​(Round to three decimal places as​ needed.)

Identify the conclusion for this hypothesis test.

A. Reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss.

B. Reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss.

C. Fail to reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss.

D. Fail to reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the responses are equivalent to a coin toss.

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

A. The result suggests that the politician is doing his best to accurately portray the feelings of the people.

B. The results are inconclusive about whether the politician is correct or not.

C. The result suggests that the politician is correct in claiming that the responses are random guesses equivalent to a coin toss.

D. The result suggests that the politician is wrong in claiming that the responses are random guesses equivalent to a coin toss.

Solutions

Expert Solution

We have to exclude 121, so we left with 488 votes in favor and 399 votes opposed

total = 488+399 = 887

So, proportion for favor = (number of votes in favor)/(total number of votes) = 488/887 = 0.55

sample proportion

population proportion po = 0.50

we need to test the claim whether the proportion of subjects who responded in favor is equal to 0.50 or not. So, it is two tailed hypothesis because the proportion of subjects who responded in favor might be less or greater than 0.50

So, we assume that the proportion is equal to 0.50 for null hypothesis and we will test it as not equal to 0.50 for alternate hypothesis

So, the following hypothesis needs to be tested

Option B is correct for hypothesis

Calculation for test statistic

we have to use z test statistic here because this is a case of proportion.

Formula for the test statistic is given as

where we have

setting the given values, we get

Now using the z distribution, looking 2.9 in column then 0.08 in row to get the p value for the two tailed test, we get

p value = 0.0029, which is less than 0.01, so it is significant.

we can reject the null hypothesis because result is significant.

we can conclude that there is enough evidence to warrant the rejection of claim that the responses are equivalent to coin toss.

option A is correct.

Since the claim is incorrect, so we can say that the result suggests that the politician is wrong in claiming that the responses are random guesses equivalent to a coin toss

So, option D is correct.


Related Solutions

Assume that adults were randomly selected for a poll. They were asked if they "favor or...
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...
Assume that adults were randomly selected for a poll. They were asked if they​ "favor or...
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,489 were in​ favor, 395 were​ opposed, and 115 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 115 subjects who said that they were​...
Assume that adults were randomly selected for a poll. They were asked if they​ "favor or...
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, 488 were in​ favor, 402 were​ opposed, and 117 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 subjects who said that they were​...
Assume that adults were randomly selected for a poll. They were asked if they​ "favor or...
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, 483483 were in​ favor, 402402 were​ opposed, and 115115 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 115115 subjects who said that they...
Assume that adults were randomly selected for a poll. They were asked if they​ "favor or...
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...
Assume that adults were randomly selected for a poll. They were asked if they "favoror oppose...
Assume that adults were randomly selected for a poll. They were asked if they "favoror oppose using federal tax dollars to fund medical research using stem cells obtained from human embryos."Of those polled,490were in favor,396were opposed,and 123were unsure. A politician claims that people don'treally understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Exclude the 123subjects who said that they were unsure,and use a 0.05 significance level to test the...
Two thousand randomly selected adults were asked if they are in favor of or against cloning....
Two thousand randomly selected adults were asked if they are in favor of or against cloning. The following table gives the responses.                                               In Favor                             Against                           No Opinion Male                                         395                                    405                                   92 Female                                     300                                    680                                    128 A.If one person is selected at random from these 2000 adults, find the probability that is person is in favor of cloning. B.If one person is selected at random from these 2000 adults, find the probability that is person is against cloning C.If one...
20. Stem Cell Survey Adults were randomly selected for a Newsweek poll. They were asked if...
20. Stem Cell Survey Adults were randomly selected for a Newsweek poll. They were asked if they “favor or oppose using federal tax dollars to fund medical research using stem cells ob- tained from human embryos.” Of those polled, 481 were in favor, 401 were opposed, and 120 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 120 subjects...
In a recent Gallup poll, 1003 randomly selected adults in the United States were asked if...
In a recent Gallup poll, 1003 randomly selected adults in the United States were asked if they have a gun in their home, and 37.2% of them answered “yes”. Construct a 95% confidence interval estimate of the percentage of all adults who would answer “yes” when asked if they have a gun in their home. [Write your answer as a complete sentence]
In a Gallup poll, 1011 adults were randomly selected and asked if they consume alcoholic beverages....
In a Gallup poll, 1011 adults were randomly selected and asked if they consume alcoholic beverages. Of this sample, 64% said they did. Check requirements before computing confidence interval If requirements are met, use StatCrunch to obtain a 90% confidence interval for the proportion of all adults who consume alcoholic beverages. c. Write interpretation of the confidence interval.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT