Confidence Intervals of Proportions

What is the margin of error for the interval (6.8, 12.9)?

• 9.85

• 3.05

• 3.50

• 6.8

Which of the following changes to a study would result in a narrower confidence interval?

• increasing the confidence level, increasing the sample size
• decreasing the confidence level, decreasing the sample size
• increasing the confidence level, decreasing the sample size
• decreasing the confidence level, increasing the sample size.

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.

• 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144
• We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. 
• 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144
• We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.

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

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)

A survey of 280 homeless persons showed that 63 were veterans.  Construct a 90% confidence interval for the proportion of homeless persons who are veterans.

• (0.161 to .289)
• (0.176 to 0.274)
• (0.184 to 0.266)
• (0.167 to 0.283)

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 gets larger
• It gets smaller
• It stays the same
• Too little information given

The 95% confidence interval for the true proportion of women shoppers who shop on impulse is (0.139, 0.201). If there were 800 women in the survey, how many reported shopping on impulse?

• 161

• 111

• 320

• 136

A study found that in a sample of 44 subjects, 9 of agree that children under 6 shouldn’t be taken to nice restaurants.

The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.

• 95% of the time the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8%.

• The population proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

• The probability that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8% is 95%.

• Based on this sample, I am 95% confident that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.