Question

The 95% confidence interval for the mean, calculated from a sample of size n = 25 is 2.233163 ≤ μ ≤ 3.966837 . Determine the sample mean X ¯ = (round to the first decimal place). Assuming that the data is normally distributed, determine the sample standard deviation s = (round to the first decimal place)

Answer 1

Lower value from confidence interval = 2.233163

Upper value from confidence interval = 3.966837

Now we find margin of error (E)

We know formula of the margin of error from Confidence interval.

C = level of confidence = 0.950 ( We converted 95 % in to decimal )

df = degree of freedom = n - 1 = 25 - 1 = 24

t(n-1 , c ) = t critical value

We look for df = 24 and c = 0.950

We look for row headed 24 and column headed 0.950

t(24 , 0.950 ) = 2.064

We use formula

Now we solve this equation for s

Round value of s up to 1 decimal place

s = 2.1

Final answer :-

s = 2.1

I hope this wil help you :)