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¯=104 Standard deviation s=10

Answer 1

Answer: For 95% Confidence Interval:

Upper Limit = 110.2

Lower Limit = 97.8

95% Confidence Interval = [97.8, 110.2]

Step-by-step explanation:

Given that,

Mean(M) = 104

Standard Deviation(SD) = 10

Sample Size(n) = 10

Formula for calculating 95% Confidence Interval are as follows:

Standard error(SE) =$\frac{SD}{\sqrt{n} }$

                         = $\frac{10}{\sqrt{10} }$

                         = 3.164

⇒ M ± $Z_{0.95}$ × SE

= 104 ± (1.96)(3.164)

= 104 ± 6.20

∴ Upper Limit = 104 + 6.20 = 110.2

   Lower Limit = 104 - 6.20 = 97.8

So,

95% Confidence Interval = [97.8, 110.2]