Proportion Interval

A recent study of 750 Internet users in Europe found that 35% of Internet users were women.  What is the 95% confidence interval of the true proportion of women in Europe who use the Internet? 

• 0.321 < p < 0.379

• 0.316 < p < 0.384

• 0.309 < p < 0.391

• 0.305 < p < 0.395

A survey of 800 women shoppers found that 17% of them shop on impulse.  What is the 98% confidence interval for the true proportion of women shoppers who shop on impulse? 

• 0.148 < p < 0.192

• 0.136 < p < 0.204

• 0.144 < p < 0.196

• 0.139 < p < 0.201

In a survey of 104 students, it was found that 79 went to the homecoming game this year. Calculate a 99% confidence interval for p.

• (0.652, 0.868)

• (0.691, 0.829)

• (0.678, 0.842(

• (0.685, 0.895)

In a survey of 104 students, it was found that 79 went to the homecoming game this year. A 99% confidence interval for p is (0.652, 0.868). Interpret this interval.

• 99% of the time the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• The probability that the population proportion of people who went to the homecoming game this year is between 65.2% and 86.6% is 95%.

• Based on this sample, I am 99% confident that the true proportion of people who went to the homecoming game this year is between 65.2% and 86.6%.

• 99% of all possible intervals calculated this way will capture the true proportion of people who went to the homecoming game this year

This is notation from a different book. Identify the confidence interval used in the figure below if each shaded area is equal to 0.05.

• 90%

• 95%

• 98%

• 99%

What is the point estimate, p̂, of this sample?

• 0.28

• 0.14

• 0.342

• 0.684

A surprising number of young adults (ages 19 to 25) still live in their parents' homes. The National Institutes of Health (NIH) surveyed independent 2253 men and 2626 women in this age group. The survey found that 986 of the men and 923 of the women lived with their parents. Find a 99% confidence interval for difference in the true proportion of men and women aged 19 to 25 who live in their parents' home.

• (0.051, 0.123)

• (0.059, 0.114)

• (0.064, 0.11)

• (0.069, 0.104)

In a Pew Research poll, 287 out of 522 randomly selected U.S. men were able to identify Egypt when it was highlighted on a map of the Middle East. When 520 randomly selected women were asked, 233 were able to do so. What is the 95% confidence interval for the difference in the true proportion of U.S. men and U.S. women who can identify Egypt on a map?

• (0.069, 0.104)

• (0.064, 0.11)

• (0.059, 0.114)

• (0.041, 0.123)

In a survey of 186 high school seniors, 17% had course work or experience in acting or play production. In another survey of 152 high school seniors, 21% had course work or experience in photography or film. Construct a 90% confidence interval for the difference between the percent of student that have photography/film and acting/play production experience.

• (-3.05, 11.05)

• (0, 11.05)

• (9.95, 24.05)

Two voting districts, C and M, were sampled to investigate voter opinion about tax spending. From a random sample of 100 voters in District C, 22 percent responded yes to the question “Are you in favor of an increase in state spending on the arts?” An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question. A 95 percent confidence interval for the difference (p_c – p_m) was calculated as -0.04 ± 0.12. Which of the following is the best interpretation of the interval?

• We are 95% confident that the majority of all voters in the state favor an increase in state spending for the arts.

• We are 95% confident that less than half of all voters in the state favor an increase in state spending for the arts.

• We are 95% confident that the difference in the proportions of all voters in districts C and M who favor an increase in state spending for the arts is between -0.16 and 0.08.

• We are 95% confident that the difference in the sample proportions of voters in districts C and M who favor an increase in state spending for the arts is between -0.16 and 0.08.

• E. We are 95% confident that the proportion of all voters in the state who favor an increase in state spending for the arts is between -0.16 and 0.08.