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

Answer:

The  90% confidence interval of the mean

(846.154, 853.846)

Step-by-step 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

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

$(850 - 1.282\frac{15}{\sqrt{25} } , 850+ 1.282 \frac{15}{\sqrt{25} })$

(850 - 3.846 , 850 + 3.846)

(846.154 , 853.846)

Final answer:-

The  90% confidence interval of the mean

(846.154, 853.846)