1. In June 2005, a survey was conducted in which a random sample of 1,464 U.S. a
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Question
1. In June 2005, a survey was conducted in which a random sample of 1,464 U.S. adults was asked the following question: "In 1973 the Roe versus Wade decision established a woman's constitutional right to an abortion, at least in the first three months of pregnancy. Would you like to see the Supreme Court completely overturn its Roe versus Wade decision, or not?"
The results were: Yes—30%, No—63%, Unsure—7% (Source: www.Pollingreport.com)
Which of the following is true about this scenario?
A: 30%, 63%, and 7% are all parameters.
B: 30%, 63%, and 7% are all statistics.
C: If another random sample of size 1,464 U.S. adults were to be chosen, we would expect to get the exact same distribution of answers.
2. A social scientist wishes to conduct a survey. She plans to ask a yes/no question to a random sample from the U.S. adult population. One proposal is to select 100 people; another proposal is to select 900 people.
Which of the following is true regarding the sample proportion p of "yes" responses?
A: The sample proportion from the sample of 900 is more likely to be close to the true population proportion, p.
B: The sample proportion from sample of 100 is more likely to be close to the true population proportion, p.
C: The sample proportion in either proposal is equally likely to be close to the true population proportion, p, since the sampling is random.
3. A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate. One plan is to select 400 voters, another plan is to select 1,600 voters.
If the study were conducted repeatedly (selecting different samples of people each time), which one of the following would be true regarding the resulting sample proportions of "yes" responses?
A: Different sample proportions would result each time, but for sample size 400 they would be centered (have their mean) at the true population proportion, whereas for sample size 1,600 they would not.
B: For either sample size, using the same size each time, as long as the samples are drawn with replacement, they would be centered (have a mean) at 0.
C: Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.
D: Different sample proportions would result each time, but for sample size 1,600 they would be centered (have their mean) at the true population proportion, whereas for sample size 400 they would not.
4. Juries should have the same racial distribution as the surrounding communities. According to the U.S. Census Bureau, 18% of residents in Minneapolis, Minnesota, are African Americans. Suppose a local court will randomly sample 100 state residents and will then observe the proportion in the sample who are African American. How likely is the resulting sample proportion to be between 0.066 and 0.294 (i.e., 6.6% to 29.4% African American)?
A: There is roughly a 68% chance that the resulting sample proportion will be between 0.066 and 0.294 of the true proportion.
B: It is certain that the resulting sample proportion will be between 0.066 and 0.294 of the true proportion.
C: There is roughly a 95% chance that the resulting sample proportion will be between 0.066 and 0.294 of the true proportion.
D: There is roughly a 99.7% chance that the resulting sample proportion will be between 0.066 and 0.294 of the true proportion.
5. A distribution of a single statistic from repeated random samples of the same size from the same population refers to which of the following?
A: Sampling distribution of a statistic
B: Distribution of population parameters
C: Random sampling
D: Distribution of summary statistics
E: The normal curve
Explanation / Answer
1. 30%, 63%, and 7% are all statistics because we found them from sample.
2. The sample proportion from the sample of 900 is more likely to be close to the true population proportion, p because as sample size increases, sample proportion becomes more close to population proportion.
3. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion because sample proportions are always centered about population proportion.
4. There is roughly a 99.7% chance that the resulting sample proportion will be between 0.066 and 0.294 of the true proportion.
mean = p=0.18
sd = sqrt[p(1-p)/n]=sqrt[0.18(1-0.18)/100]=0.038
mean - 3sd = 0.18 - 3(0.038) = 0.066
mean + 3sd = 0.18 + 3(0.038) = 0.294
and according to empirical rule, 99.7% proportions lie within 3 standard deviations from mean.
5. A distribution of a single statistic from repeated random samples of the same size from the same population refers to Sampling distribution of a statistic.
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