Question

step by step please.

It is reported that a 95% confidence interval for the population average of a variable X normally distributed is [37.1;46.9]. Consider that the population standard deviation is 12.5 and that the interval was obtained considering a population of infinite size. If P (Z> 1.96) = 0.025, what is the sample size used in this study?

Answer 1

Given that the confidecne interval is [37.1 , 46.9]

Confidene Inteval for the population variable X = [ - Marging of Error, + Margin of error]

where x = Sample Mean

So here

- Marging of Error = 37.1

+ Margin of error = 46.9

Solving the two equations we get

= 42 and Margin of error = 4.9

We know that Margin of error = Z-score * ( / )

Here Given  P (Z> 1.96) = 0.025, So Z-score = 1.96

Population Standard deviation = 12.5

We already got the Marging of error as 4.9

n is the sample size

4.9 = 1.96 * (12.5 / )

= (1.96 * 12.5) / 4.9

= 24.5 / 4.9

= 5

n = 52

n = 25

So Sample size used in the study = 25