Question

Use the given data to find the 95% confidence interval estimate of the population mean μ. Assume that the population has a normal distribution. IQ scores of professional athletes: Sample size n=10 Mean x¯=106 Standard deviation s=12

______<μ<________

Answer #1

solution :

Given that,

= 106

s = 12

n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t_{
/2,df} = t_{0.025,9} =2.262

Margin of error = E = t_{/2,df}
* (s /n)

= 2.262* (12 / 10) = 8.58

The 95% confidence interval estimate of the population mean is,

- E < < + E

106 - 8.58 < < 106 + 8.58

97.42< < 114.58

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