Quiz 10.1A AP Statistics Name: Suppose you administer a certain aptitude test to a simple random sample of 9 students in your school, and that the average score is 105. From past experience, scores on such a test among students like those at your school follow a Normal distribution. We want to determine the mean score µ of the population. Assume a standard deviation of = 15 for the test. 1. What is the upper critical value for a 98% confidence interval? (Show the key numbers in the sketch of the distribution.) 2. Construct and interpret a 98% confidence interval for the mean score µ. Follow the Inference Toolbox. 3. Explain the meaning of 98% confident. 4. What sample size would be needed to have a margin of error of at most 4 points (still with 98% confidence)? Show your work.
Quiz 10.1B AP Statistics Name: Suppose your class is investigating the weights of Snickers 1-ounce Fun-Size candy bars to see if customers are getting full value for their money. Assume that the weights are Normally distributed with standard deviation = 0.005 ounces. Several candy bars are randomly selected and weighed with sensitive balances borrowed from the physics lab. The weights are 0.95 1.02 0.98 0.97 1.05 1.01 0.98 1.00 ounces. We want to determine a 90% confidence interval for the true mean, µ. 1. Determine z*. (Show your work, including a sketch of the distribution.) 2. Calculate and interpret a 90% confidence interval for the mean weight of the candy bars. Follow the Inference Toolbox. 3. Explain the meaning of the confidence level. 4. Determine the sample size you would need to estimate µ within 0.001 at a 90% confidence level.
Quiz 10.2A AP Statistics Name: National Fuelsaver Corporation manufactures the Platinum Gasaver, a device they claim may increase gas mileage by 22%. Here are the percent changes in gas mileage for 15 identical vehicles, as presented in one of the company s advertisements: 48.3 46.9 46.8 44.6 40.2 38.5 34.6 33.7 28.7 28.7 24.8 10.8 10.4 6.9 12.4 1. Construct and interpret a 90% confidence interval to estimate the mean fuel savings in the population of all such vehicles. Follow the Inference Toolbox. 2. Explain what 90% confidence means in this setting. 3. Comment on the manufacturer s claim based on your work in Question 1.
Quiz 10.2B AP Statistics Name: About 42,000 high school students took the AP Statistics exam in 2001. The free-response section of the exam consisted of five open-ended problems and an investigative task. Each free-response question is scored on a 0 to 4 scale (with 4 being the best). A random sample of 25 student papers yielded the following scores on one of the free-response questions: 1 0 1 0 0 0 3 1 1 1 0 2 0 0 2 1 1 0 2 4 1 0 2 0 3 1. Is a sample of 25 papers large enough to provide a good estimate of the mean score of all 42,000 students on this exam problem? Justify your answer. 2. Do you think the population of scores on this question is Normally distributed? Explain why or why not. 3. Construct and interpret a 95% confidence interval for the mean score on this exam question. Follow the Inference Toolbox. Be sure to explain why it s okay to calculate the interval in light of your answer to Question 2.
Quiz 10.3A AP Statistics Name: A New York Times poll on women s issues interviewed 1025 women randomly selected from the United States, excluding Alaska and Hawaii. The poll found that 47% of the women said they do not get enough time for themselves. 1. The poll announced a margin of error of ±3 percentage points for 95% confidence in its conclusions. Do you agree with this margin of error? If so, explain why. If not, tell why not. 2. What is the 95% confidence interval from this poll result? Interpret the interval in context. 3. What conditions must be met in order for the confidence interval in Question 2 to be valid? Check whether each of those conditions is satisfied in this case. 4. Explain to someone who knows no statistics why we can t just say that 47% of all adult women do not get enough time for themselves. 5. Explain clearly what 95% confidence means.
Quiz 10.3B AP Statistics Name: A news article on a Gallup Poll noted that 28 percent of the 1548 adults questioned felt that those who were able to work should be taken off welfare. The article also said, The margin of error for a sample size of 1548 is plus or minus three percentage points. 1. Opinion polls usually announce margins of error for 95% confidence. Using this fact, explain to someone who knows no statistics what margin of error plus or minus three percentage points means. 2. Do you agree with the margin of error stated in the poll results? If so, explain why. If not, tell why not. 3. What is the 99% confidence interval from this poll? Interpret the interval in context. 4. What conditions must be met in order for the confidence interval in Question 3 to be valid? Check whether each of those conditions is satisfied in this case. 5. This poll was conducted by telephone. Explain how undercoverage could lead to a biased estimate in this case.