Question

A random sample of 25 items is drawn from a population. The sample mean is 850 and population standard deviation is 15. Find a 90% confidence interval

Answer 1

The 90% confidence interval of the mean

(846.154, 853.846)

Explanation:

Step(i):-

Given that the sample size 'n' = 25

Given that the sample mean (x⁻) = 850

The standard deviation of the Population (σ) = 15

Level of significance = 0.10

Step(ii):-

The 90% confidence interval is determined by

`(x^(-) - Z_(0.05) (S.D)/(√(n) ) , x^(-) + Z_(0.05) (S.D)/(√(n) ) )`

`(850 - 1.282(15)/(√(25) ) , 850+ 1.282 (15)/(√(25) ))`

(850 - 3.846 , 850 + 3.846)

(846.154 , 853.846)

Final answer:-

The 90% confidence interval of the mean

(846.154, 853.846)