Introduction to Confidence Intervals Answers

A newspaper poll found that 54% of the respondents in a random sample of voters in the city plan to vote for candidate Roberts. A 95 percent confidence interval for the population proportion is 0.54 ± 0.06. Based on this interval, what can the newspaper report?

A credit card company is interested in the proportion of its customers who pay their minimum balance on time. The company randomly sampled 500 records from the previous month. The 95% confidence interval for the true proportion of customers who pay on time was (0.765, 0.835). What are the point estimate and the margin of error for this interval?

A study was done to estimate the mean commute time for a population of employed adults. A random sample of 25 employed adults in a particular city was taken, and the 95% confidence interval for mean commute time was calculated to be 34.42 ± 8.14 minutes. A councilman is advocating for road repairs and states that, in this city, people with jobs commute an average of 45 minutes to work each day. Does the confidence interval justify the councilman’s statement?

A researcher for a polling organization used a random sample of 1,540 residents in a city to construct a 95 percent confidence interval for the proportion of voters who would vote for candidate Jones. The resulting confidence interval was 0.480 ± 0.025. What is the correct interpretation of the confidence interval?

A clinic measured the systolic blood pressure for a random sample of 10 patients. The resulting 95% confidence interval for the mean systolic blood pressure of all the patients at this clinic was (111.3, 129.5). What was the mean systolic blood pressure from the sample of 10 patients?

A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90% confidence interval for the true mean weight of bags of grapes from this store to be (15.875, 16.595) ounces. Is the store justified in stating that the average weight of the bags of grapes is 16 ounces?

A clinic measured the systolic blood pressure for a random sample of 10 patients. The resulting 95% confidence interval for the mean systolic blood pressure of all the patients at this clinic was (111.3, 129.5). What was the margin of error for this confidence interval?

A yogurt company claims that it prints a free yogurt coupon under a randomly selected 20% of its lids. A loyal customer purchases 85 yogurt cups, and records whether each was a winner. After consuming all 85 cups, he is disappointed to see that only 12 (14.1%) of his yogurt cups contained coupon codes. He performs a 99% confidence interval for the proportion of yogurt cups containing coupon codes, obtaining (0.044, 0.238). What conclusion can the customer draw about the yogurt company’s claim?

Twenty-four pairs of adult brothers and sisters were sampled at random from a population. The difference in heights, recorded in inches (brother’s height minus sister’s height), was calculated for each pair. The 95% confidence interval for the mean difference in heights for all brother-and-sister pairs in this population was (–0.76, 4.34). What was the sample mean difference from these 24 pairs of siblings?

An inspector inspects large truckloads of potatoes to determine the proportion with blemishes prior to using the potatoes to make potato chips. She intends to compute a 95% confidence interval for this proportion. To do so, she selects a simple random sample of 90 potatoes, and finds 12 with blemishes. The 95% confidence interval is (0.063, 0.204). What is the correct interpretation for this confidence interval?