Question

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 womans 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. question 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 p̂ 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.

Explanation:

Step1: Recall parameter and statistic definitions

Parameters describe a population, and statistics describe a sample. The 30%, 63%, and 7% are based on a sample of 1464 U.S. adults, so they are statistics.

Step2: Analyze sampling variability

If another sample of size 1464 is taken, due to sampling variability, we would not expect to get the exact same distribution of answers.

For the second - question:

Step1: Understand the relationship between sample size and accuracy

Larger sample sizes tend to give sample statistics that are closer to the true population parameters. A sample of 900 people is larger than a sample of 100 people. So the sample proportion from the sample of 900 is more likely to be close to the true population proportion.

Answer:

Question 1: B. 30%, 63%, and 7% are all statistics.
Question 2: A. The sample proportion from the sample of 900 is more likely to be close to the true population proportion, p.