The Gallup organization conducted a phone survey from June 9-12, 2011. Researchers at Gallup chose a random sample of 1020 American adults, age 18 or older who lived in the continental U.S. The random sample of adults were selected using random digit dial sampling. This means that a computer randomly dialed phone numbers. Approximately 400 cell phones and 600 landlines were selected in the sample. The 1020 American adults were asked to respond to the following question: “Please tell me how much confidence you, yourself, have in banks.” Gallop reported that 36% of the 1,020 adults indicated that they had very little or no confidence in banks. The margin of error was estimated to be 2.8%.
A researcher wanted to estimate the actual percentage of all American adults who had very little or no confidence in banks from June 9-12, 2011. Based on the survey results, which of the following is the best estimate of the actual percentage of all American adults who had very little or no confidence in banks from June 9-12, 2011?
A.
95.0%
B.
38.8%
C.
36.0%
D.
41.6%
Based on the survey results, the best estimate of the actual percentage of all American adults who had very little or no confidence in banks is 36.0%. The survey reported that 36% of the 1,020 adults indicated this, so this percentage is the most accurate estimate. Therefore, the correct answer is C. 36.0%.
A certain manufacturer makes candy. Its brown candy is very popular. There are always brown candies in the candy bags. The manufacturer claims that the bags of candy will have about 50% brown candies. Sam plans to buy a large family size bag of these candies and Kerry plans to buy a small fun-size bag. Whose bag is more likely to have more than 70% brown candies?
A.
Kerry’s, because there is more variability in the proportion of brown candies among smaller samples.
B.
Sam’s, because there is more variability in the proportion of brown candies among larger samples.
C.
Both have the same chance because both are random samples.
The correct answer is A. Kerry's bag is more likely to have more than 70% brown candies. This is because there is more variability in the proportion of brown candies among smaller samples. The larger the sample size, the closer it is likely to be to the population proportion (in this case, 50% brown candies). Smaller sample sizes are more likely to deviate from the population proportion, so Kerry's small fun-size bag has a higher chance of having a proportion of brown candies that is significantly different from 50%.
The Associated Press (Dec. 16, 1991) reported that in a random sample of 507 adult U.S. citizens, only 142 could correctly identify the Bill of Rights as the first ten amendments to the U.S. Constitution. If we calculate a 90% confidence interval for the proportion of adult U.S. citizens who could correctly identify the Bill of Rights in December, 1991., the interval is (0.247, 0.313).
True
False
True.
A 90% confidence interval (0.247, 0.313) means that we are 90% confident that the true proportion of adult U.S. citizens who could correctly identify the Bill of Rights lies within this interval.
A computer-gaming entrepreneur who develops and sells new games to major manufacturers of systems such as Xbox™, Wii™, and PS3™ wants to estimate the percentage of households with teenagers, that own any of these gaming systems. The entrepreneur randomly selects 500 households with teenagers and performs a survey to determine whether or not each household owns an Xbox™, Wii™, PS3™, or some similar system. He determines that 421 of the households he surveyed own such systems.
Compute the confidence interval estimate for the proportion of the general population of households with teenagers that own a gaming system. Use a 95% confidence level. Then determine whether the conclusion below is true or false.
Conclusion: The confidence interval is determined to be (0.810, 0.874). This means that the entrepreneur is 95% confident that between 81.0% and 87.4% of all households with teenagers own an Xbox™, Wii™, PS3™, or some similar system.
True
False
The conclusion is True.
A 95% confidence interval (0.810, 0.874) means that we are 95% confident that the true proportion of all households with teenagers that own a gaming system falls within this interval. Therefore, the entrepreneur can be 95% confident that between 81.0% and 87.4% of households with teenagers own a gaming system.