Chapter Test 341 Chapter Test 6 Take this test as you would take a test in class. 1. In a survey of 2096 U.S. adults, 1740 think football teams of all levels should require players who suffer a head injury to take a set amount of time off from playing to recover. (Adapted from The Harris Poll) (a) Find the point estimate for the population proportion. (b)Construct a 95% confidence interval for the population proportion. Interpret the results. (c) Would it be unusual for the population mean to be 80%? Explain. (d)Find the minimum sample size needed to estimate the population proportion at the 99% confidence level to ensure that the estimate is accurate within 3% of the population proportion. 2. The data set represents the weights (in pounds) of 10 randomly selected black bears from northeast Pennsylvania. Assume the weights are normally distributed. (Source: Pennsylvania Game Commission) 170 225 183 137 287 191 268 185 211 284 (a) Find the sample mean and the sample standard deviation. (b) Construct a 95% confidence interval for the population mean. Interpret the results. (c)Construct a 99% confidence interval for the population standard deviation. Interpret the results. 3. The data set represents the scores of 12 randomly selected students on the SAT Physics Subject Test. Assume the population test scores are normally distributed and the population standard deviation is 108. (Adapted from The College Board) 590 650 730 560 460 400 620 780 510 700 590 670 (a) Find the point estimate of the population mean. (b) Construct a 90% confidence interval for the population mean. Interpret the results. (c) Would it be unusual for the population mean to be under 575? Explain. (d) Determine the minimum sample size required to be 95% confident that the sample mean test score is within 10 points of the population mean test score. 4. Use the standard normal distribution or the t-distribution to construct the indicated confidence interval for the population mean of each data set. Justify your decision. If neither distribution can be used, explain why. Interpret the results. (a) In a random sample of 40 patients, the mean waiting time at a dentist’s office was 20 minutes and the standard deviation was 7.5 minutes. Construct a 95% confidence interval for the population mean. (b) In a random sample of 15 cereal boxes, the mean weight was 11.89 ounces. Assume the weights of the cereal boxes are normally distributed and the population standard deviation is 0.05 ounce. Construct a 90% confidence interval for the population mean.
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