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22. A random sample of 50 college textbooks gave a mean price of $130.50 with a standard deviation of $22.75. Construct a 95% confidence interval for the mean price of all college textbooks and write an interpretation in context. 23. Pew Research conducted a survey of 2054 randomly selected U.S. adults and found that 1063 of these surveyed adults played video games. Construct a 95% confidence interval for the proportion of all U.S. adults who play video games, and write an interpretation in context. 24. A simple random sample of 30 students at a local community college 437 321 216 452 162 who were Facebook users was collected and each student's number of 310 395 239 508 426 Facebook friends was recorded in the table given. A 9% confidence 284 93 300 99 240 interval for the average number of Facebook friends is to be constructed. 137 368 101 279 205 a. What initial conditions need to be met before the 99% confidence 532 214 363 194 362 interval is constructed? 416 290 252 253 406 b. If the initial conditions are met, construct a 99% confidence interval for the mean number of Facebook friends of all Facebook users at this community college. Round your answer to the nearest whole number. Write an interpretation of the confidence interval in context. c. Would a 95% confidence interval be wider or narrower than the 99% confidence interval you found in part (b)? d. If a random sample of size 50 were collected that happened to have the same mean and sample standard deviation as the sample above, would a 99% confidence interval using this sample of size 50 be wider or narrower than the confidence interval found in part (b)