Question

Use the given data to find the 95% confidence interval estimate of the population mean ?. Assume that the population has a normal distribution.

IQ scores of professional athletes:

Sample size ?=25

Mean ?⎯⎯⎯=106

Standard deviation ?=11

________<?__________

Answer 1

Solutions:

Gien that
n=25,
x̄=106
S=11
(1-α)%= 95%
1-α= 0.95
α= 0.05
α/2=0.025
t(α/2),(n-1)=t(0.025),(25-1)
=t(0.025),(24)=2.064..... From students t table.
Margin of error=t(α/2),(n-1) ×( S /✓n)
= (2.064)×(11/✓25)
=2.064×2.2

= 4.5408
95% confidence interval estimate of the population mean ? is given as,
x̄ ± Margin of error=(106-4.5408 ,106+4.5408)

=(101.4592,110.5408)

Lower limit: 101.4592

Upper limit:110.5492

95% confidence interval estimate of the population mean is 101.4592<?<110.5408)