Question

Suppose 150 students are randomly sampled from a population of college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 99% confidence interval for the average IQ of college students? Possible Answers: 1) A) E =1.21 B) E = 1.25 C) E =2.52 D) E = 2.11 2) A) 112.48 < μ < 117.52 B) 113.79 < μ < 116.21 C) 112.9 < μ < 117.10 D) 113.75 < μ < 116.3

Answer 1

Answer:

99% confidence interval for the mean of college students

A) 112.48 < μ < 117.52

Step-by-step explanation:

step(i):-

Given sample size 'n' =150

mean of the sample = 115

Standard deviation of the sample = 10

99% confidence interval for the mean of college students are determined by

$(x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )$

Step(ii):-

Degrees of freedom

ν = n-1 = 150-1 =149

t₁₄₉,₀.₀₁ =  2.8494

99% confidence interval for the mean of college students are determined by

$(115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )$

on calculation , we get

(115 - 2.326 , 115 +2.326 )

(112.67 , 117.326)