Question

Professor Snape would like you to construct confidence intervals for the following random sample of eight (8) golf scores for a particular course he plays. This will help him figure out his true (population) average score for the course.

Golf scores: 95; 92; 95; 99; 92; 84; 95; and 94.

What are the sample mean and sample standard deviation? (Round your answers to three decimal places.)

=

=

What are the following confidence intervals? (Round your answers to three decimal places.)

85% CI: LCL =

85% CI: UCL =

98% CI: LCL =

98% CI: UCL =

Answer 1

a)
sample mean, xbar = 93.25
sample standard deviation, s = 4.334

b)
sample size, n = 8
degrees of freedom, df = n - 1 = 7

Given CI level is 85%, hence α = 1 - 0.85 = 0.15
α/2 = 0.15/2 = 0.075, tc = t(α/2, df) = 1.617

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (93.25 - 1.617 * 4.334/sqrt(8) , 93.25 + 1.617 * 4.334/sqrt(8))
CI = (90.772 , 95.728)

85% CI: LCL =90.772 ,

85% CI: UCL =95.728

c)
Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.998

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (93.25 - 2.998 * 4.334/sqrt(8) , 93.25 + 2.998 * 4.334/sqrt(8))
CI = (88.656 , 97.844)

98% CI: LCL =88.656 ,

98% CI: UCL =97.844