Estimating With Confidence Practice

AP STATISTICS | Confidence Intervals | Practice Handout  Jan. 15  

1. A balanced scale? To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are normally distributed with unknown mean (this mean is 10 grams if the scale has no bias). The standard deviation of te scale readings is known to be 0.0002 gram. a) The weight is weighed five times. The mean result is 10.0023 grams. Construct and interpret a 98% confidence interval for the mean of repeated measurements of the weight. b) How many measurements must be averaged to get a margin of error +- 0.0001 with 98% confidence? Show your work. 2. Confidence Level and Margin of Error High school students who take the SAT Mathematics exam a second time generally score higher than on their first try. The change in score has a normal distribution with standard deviation σ = 50. A random sample of 1000 students gain an average of x = 22 points on their second try. a) Construct and interpret a 95% confidence interval for the mean score gain μ in the population. b) Calculate the 90% and 99% confidence intervals for μ . c) Make a sketch to compare these three intervals. How does increasing the confidence level affect the length of the confidence interval? 3. The 2004 Presidential Election A closely contested presidential election pitted George W. Bush against John Kerry in 2004. A poll taken immediately before the 2004 election showed that 51% of the sample intended to vote for Kerry. The polling organization announced that they were 95% confident that the sample result was within +- 2 points of the true percent of all voters who favored Kerry. a) Explain in plain language to someone who knows no statistics what “95% confident” means in this announcement. b) The poll showed Kerry leading. Yet the polling organization said the election was too close to call. Explain why. c) On hearing the poll, a nervous politician asked, “What is the probability that over half the voters prefer Kerry?” A statistician replied that this question can’t be answered from the poll results, and that it doesn’t even make sense to talk about such a probability. Explain why.