Question

A simple random sample of 80 items from a population with o = 7 resulted in a sample mean of 37. If required, round your answers to two decimal places. a. Provide a 90% confidence interval for the population mean. to b. Provide a 95% confidence interval for the population mean. to c. Provide a 99% confidence interval for the population mean. to

Answer 1

The solution to this problem is given by

Solution Given data is Sample size an = 80 Population S.D = 0 27 Sample Mean ał = 37 (a) The 90.1. CI for population mean is given by 22 = 1.645 Where 22 q core & t z 0.05 / In 37 + 1.64587 180 37 t 1.287 N (37 + 11287, 37 – 1.287) (35.713, 38.287) (35.71, 38.29) (Rounded value) 35.71 to 38.297

(b) The 95). (I for population mean is given by x + 1.96 6/18 [whe here 1.96=20025 37 I 1.964 √80 37 + 1.533 (37-1.533, 37 + 1,533) (35.467 , 38.533) 135.47 3 38.53) 7 Rounded value) to 138.531 35. 47

(C) The 99% CI for population given by mean is where Zdg X + 2, Jh = 2 0.005 2.575 - Ha 3 37 + 2.575 X 7 180 ( 37 £ 9.015) (37 – 2015 , 37 + 2.015) (34.985, 39.015) (34.98, 39,01) (Rounded value) 2 34.98 to 139.01