8. [-/4.42 Points] DETAILS BBUNDERSTAT12 7.3.012.MI.S. MY NOTES ASK YOUR TEACHER For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 518 judges, it was found that 279 were introverts. LA USE SALT (a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.) (b) Find a 99% confidence interval for p. (Round your answers to two decimal places.) lower limit upper limit Give a brief interpretation of the meaning of the confidence interval you have found. O We are 1% confident that the true proportion of judges who are introverts falls within this interval. O We are 99% confident that the true proportion of judges who are introverts falls outside this interval. We are 99% confident that the true proportion of judges who are introverts falls within this interval. O We are 1% confident that the true proportion of judges who are introverts falls above this interval. (c) Do you think the conditions np > 5 and nq > 5 are satisfied in this problem? Explain why this would be an important consideration. O Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal. No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately binomial. O Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial.9. [-14.42 Points] DETAILS BBUNDERSTAT12 7.4.0145. MY NOTES ASK YOUR TEACHER Independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric. Weights (in lb) of pro football players: x1; :11 = 21 243 263 256 251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265 271 Weights (in lb) of pro basketball players: x2; :12 = 19 202 200 220 210 192 215 222 216 228 207 225 208 195 191 20? 196 133 193 201 [9 USE SALT (a) Use a calculator with mean and standard deviation keys to calculate i1, 51' x2, and 52. (Round your answers to four decimal places.) (b) Let 1'1 be the population mean for x1 and let #2 be the population mean for x2. Find a 99% condence interval for F1 #2. (Round your answers to one decimal place.) lower limit E E upper limit (c) Examine the condence interval and explain what it means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, do professional football players tend to have a higher population mean weight than professional basketball players? 0 Because the interval contains only negative numbers, we can say that professional football players have a lower mean weight than professional basketball players. 0 Because the interval contains both positive and negative numbers, we cannot say that professional football players have a higher mean weight than professional basketball players. 0 Because the interval contains only positive numbers, we can say that professional football players have a higher mean weight than professional basketball players. (d) Which distribution did you use? Why? 0 The standard normal distribution was used because 0-1 and 0-2 are unknown. 0 The standard normal distribution was used because 0'1 and 0-2 are known. 0 The Student's tdistribution was used because 0'1 and 0-2 are known. 0 The Student's t-distribution was used because 0-1 and 02 are unknown