Question

Neatly show all work necessary for a complete solution of each problem. 1. The values below form a simple random sample from a population with a normal dis- tribution. Find a 95 % confidence interval for the population mean. 30, 28, 24, 36, 18, 26, 32, 22 answer 2. In a simple random sample of 190 of a college's alumni, 63 have returned to campus for Homecoming at least onoe. Find a 99% confidence interval for the proportion of all alumni who have returned. answer 9% ConTr Gorf

Answer 1

Solution: Given that samples : 30,28,24,36,18,26,32,22
X = 27, s = 5.757, n = 8, 95% Confidence interval
df = n-1 = 7, t = 2.365

95% Confidence interval for the mean = X +/- t*s/sqrt(n)
= 27 +/- 2.365*5.757/sqrt(8)
= (22.1863 , 31.8137)

-------------------------------
Solution: that sample n = 190, x = 63, 99% Confidence interval for Z = 2.576
p = x/n = 63/190 = 0.33,
q = 1-p = 1-0.33 = 0.67

99% Confidence interval for the population proportion = p +/- Z*Sqrt(pq/n)
= 0.33 +/- 2.576*sqrt(0.33*0.67/190)
= (0.2421 , 0.4179)