Intro to Proportion Confidence Intervals

A research company wants to estimate the proportion of people who like oatmeal. They want the confidence level to be 95%. The company gets 325 people to sign up for the survey, but on the day that the survey is issued, only 250 people show up and take the survey. What happens to the confidence interval?

• It stays the same

• It gets narrower

• It gets wider

• Not enough information

A __________ gives an interval of plausible values for the _____________. 

• confidence interval, statistic

• point estimate, parameter

• point estimate, statistic

• confidence interval, parameter

Suppose that a 95% confidence interval for hours worked by students was computed to be (8.82, 10.78). Which of these is a valid interpretation of this confidence interval?

• There is a 95% probability that the average number of hours worked by all students is between 8.82 and 10.78 hours.

• There is a 95% probability that a randomly selected student worked between 8.82 and 10.78 hours.

• We are 95% confident that the population average number of hours worked by all students is between 8.82 and 10.78 hours.

• We are 95% confident that the average number of hours worked by the students in our sample is between 8.82 and 10.78 hours.

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

Sanjay is researching if female students are more or less likely than male students to have received extra credit at a large university. He takes a random sample of 300 students. Sanjay used this sample to build a 95% confidence interval to estimate the difference between the proportion of females and males receiving extra credit. The resulting interval was 0.05±0.07. Based on the interval, what do we know about the corresponding P-value and conclusion at the α=0.05 level of significance?

• The P-value is less than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is less than α=0.05, and he should conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he should conclude that there is a difference between the proportions.

Sanjay is researching if female students are more or less likely than male students to have received extra credit at a large university. He takes a random sample of 300 students. Sanjay used this sample to build a 95% confidence interval to estimate the difference between the proportion of females and males receiving extra credit. The resulting interval was 0.05±0.07. Based on the interval, what do we know about the corresponding P-value and conclusion at the α=0.05 level of significance?

• The P-value is less than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is less than α=0.05, and he should conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he should conclude that there is a difference between the proportions.

It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets.  What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets? 

• (0.621, 0.780)

• (0.591, 0.812)

• (0.584, 0.830)

• (0.615, 0.805)

Which of the following actions would produce a confidence interval with a smaller width assuming all other contingencies remained constant?

• Using a higher confidence level

• Using a lower confidence level

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 researcher at a major hospital wishes to estimate the proportion of the adult population of the U.S. that has high blood pressure.  How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%?

• 9

• 271

• 164

• 542