Question

How many rounds of golf do those physicians who play golf play per year? A survey of 12 physicians revealed the following numbers:

6,43,17,1,36,42,22,13,15,31,10,496,43,17,1,36,42,22,13,15,31,10,49

Estimate with 91% confidence the mean number of rounds played per year by physicians, assuming that the population is normally distributed with a standard deviation of 7.

Note: For each confidence interval, enter your answer in the form (LowerConf, UpperConf). You must include the parentheses and the comma between the confidence limits.

Answer 1

sample mean = sum of all number/ toatal number
= (6 +43 + 17 + 1 + 36 + 42 + 22 + 13 + 15 + 31 + 10 + 49)/12

sample mean, xbar = 23.75
sample standard deviation, σ = 7
sample size, n = 12

Given CI level is 91%, hence α = 1 - 0.91 = 0.09
α/2 = 0.09/2 = 0.045, Zc = Z(α/2) = 1.7

Critical value is calculated using excel as:
=NORM.INV(0.045,0,1)

ME = zc * σ/sqrt(n)
ME = 1.7 * 7/sqrt(12)
ME = 3.44

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (23.75 - 1.7 * 7/sqrt(12) , 23.75 + 1.7 * 7/sqrt(12))
CI = (20.31 , 27.19)