Question

a random sample of n=24 data from a normal distribution with unkown variance produced x=42.5 and s=26 what is the 95 confidence interval

Answer 1

Answer:

95% of confidence intervals are

(31.5215 , 53.4785)

Step-by-step explanation:

Explanation:-

Given sample size 'n' =24

Mean of the sample  x⁻ = 42.5

Standard deviation of the sample 'S' = 26

95% of confidence intervals are determined by

$(x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} })$

Degrees of freedom

                ν =n-1 = 24-1 =23

$t_{0.05} = 2.0686$

95% of confidence intervals are

$(42.5 - 2.0686 \frac{26}{\sqrt{24} } , 42.5+ 2.0686 \frac{26}{\sqrt{24} })$

( 42.5 -10.9785 ,42.5 +10.9785)

(31.5215 , 53.4785)