Difference of proportions review

• I only

• II only

• III only

• I and II only

• I, II, and III

• 0.1398

• 0.2843

• 0.4315

• 0.5685

• 0.7157

• $p_a-p_b$

• $\frac{p_a}{50}-\frac{p_b}{100}$

• 
• $\frac{p_a\left(1-p_a\right)}{50}+\frac{p_b\left(1-p_b\right)}{100}$

• $\sqrt{\frac{p_a\left(1-p_a\right)}{50}+\frac{p_b\left(1-p_b\right)}{100}}$

• Days

• Dollars

• Companies

• Workers

• There are no units associated with the mean of a sampling distribution

Consider a 95 percent confidence interval constructed for the difference between two population proportions  $p_R-p_S$   is given as (-0.05, 0.15). Which of the following is an appropriate interpretation of the confidence interval? 

• In repeated random sampling with the same sample size,  $p_R^{\Delta}-p_S^{\Delta}$   will be contained in the interval approximately 95 percent of the time.

• In repeated random sampling with the same sample size,  $p_R$   will be contained in the interval approximately 95 percent of the time.

• In repeated random sampling with the same sample size,  $p_R^{\Delta}$   will be contained in the interval approximately 95 percent of the time.

• The probability is 0.95 that the difference in the sample proportions  $p_R^{\Delta}-p_S^{\Delta}$  is between −0.05 and 0.15.

• In repeated random sampling with the same sample size, approximately 95 percent of the intervals will capture the difference in population proportions,  $p_R-p_S$  .

A recent study was conducted in which a random sample of men and a random sample of women were surveyed about whether they were fans of a professional football team. The study found that 39 percent of men in the sample were fans and 22 percent of women in the sample were fans. A 99 percent confidence interval for the difference in the proportion of fans of a professional football team between men and women was reported as (0.133,0.207)

. Which of the following statements is the best interpretation of the interval?

• The difference in the percents of fans of a professional football team between men and women is 17%.

• There is a 99% chance of finding a difference between 13.3% and 20.7% for the percents of men and women who are fans of a professional football team.

• We are 99% confident that the percent of men who are fans of a professional football team exceeds that of women by at least 20.7%.

• We are 99% confident that the difference in the sample percents of men and women who are fans of a professional football team is between 13.3% and 20.7%.

• We are 99% confident that the difference in the population percents of all men and women who are fans of a professional football team is between 13.3% and 20.7%.

The manager of a symphony in a large city wants to investigate music preferences for adults and students in the city. Let  $p_A$  represent the population proportion of adults who live in the city who prefer pop music. Let  $p_S$   represent the population proportion of students who live in the city who prefer pop music. Random samples of 200 adults from the city and 200 students from the city will be selected.

• The difference between the population proportion of adults who prefer pop music and the population proportion of students who prefer pop music is approximately 0.022.

• The difference between the population proportion of adults who prefer pop music and the population proportion of students who prefer pop music is 0.

• For all random samples of 200 adults from the city and 200 students from the city, the difference between the sample proportion of adults who prefer pop music and the sample proportion of students who prefer pop music will be 0.022.

• For all random samples of 200 adults from the city and 200 students from the city, the difference between the sample proportion of adults who prefer pop music and the sample proportion of students who prefer pop music will be 0.

• For all random samples of 200 adults from the city and 200 students from the city, the sample proportion of adults who prefer pop music will be greater than the sample proportion of students who prefer pop music in about 2.2% of samples.

Suppose that 25 percent of women and 22 percent of men would answer yes to a particular question. In a simulation, a random sample of 100 women and a random sample of 100 men were selected, and the difference in sample proportions of those who answered yes, p̂women - p̂men, was calculated. The process was repeated 1,000 times. Which of the following is most likely to be a representation of the simulated sampling distribution of the difference between the two sample proportions?

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