Question

A simple random sample of size n is drawn. The sample​ mean, x overbar​, is found to be 19.5​, and the sample standard​ deviation, s, is found to be 4.6. ​(a) Construct a 95​% confidence interval about mu if the sample​ size, n, is 35. Lower​ bound: nothing​; Upper​ bound: nothing ​(Use ascending order. Round to two decimal places as​ needed.) ​(b) Construct a 95​% confidence interval about mu if the sample​ size, n, is 61. Lower​ bound: nothing​; Upper​ bound: nothing ​(Use ascending order. Round to two decimal places as​ needed.) How does increasing the sample size affect the margin of​ error, E? A. The margin of error increases. B. The margin of error does not change. C. The margin of error decreases. ​(c) Construct a 99​% confidence interval about mu if the sample​ size, n, is 35. Lower​ bound: nothing​; Upper​ bound: nothing ​(Use ascending order. Round to two decimal places as​ needed.) Compare the results to those obtained in part​ (a). How does increasing the level of confidence affect the size of the margin of​ error, E? A. The margin of error increases. B. The margin of error decreases. C. The margin of error does not change. ​(d) If the sample size is 18​, what conditions must be satisfied to compute the confidence​ interval? A. The sample size must be large and the sample should not have any outliers. B. The sample data must come from a population that is normally distributed with no outliers. C. The sample must come from a population that is normally distributed and the sample size must be large. Click to select your answer(s).

Answer 1