Question

Can you please explain me this question? Thanks!

Construct a 95% confidence interval for the mean of a population if n=25, x̅= 42.3 and σ= 3.2. Assume the mean is normally distributed.

Answer 1

ANSWER:

Given that,

Construct a 95% confidence interval for the mean of a population if n=25, x̅= 42.3 and σ= 3.2. Assume the mean is normally distributed.

n = 25

x̅= 42.3

σ = 3.2

c = 95% = 95/100 = 0.95

= 1-c = 1-0.95 = 0.05

/2 = 0.05/2 = 0.025

Critical value = = = 1.645

95% confidence interval

95% CI = x̅ *(σ/sqrt(n))

95% CI = 42.3 1.645 *(3.2/sqrt(25))

95% CI = 42.3 1.0528

95% CI = 42.3-1.0528 , 42.3+1.0528

95% CI = 41.2472 , 43.3528

Assume the mean is normally distributed

41.2472 <   < 43.3528

----------------------------------------------------------------------The End ------------------------------------------------------------------------

If you have any doubt please ask me friend and if you are satisfied with my solution please give me thumb up.