Question

A simple random sample of size n is drawn. The sample​ mean,

x overbarx​,

is found to be

18.4,

and the sample standard​ deviation, s, is found to be

4.9

Construct a

95​%

confidence interval about

muμ

if the sample​ size, n, is

35.

find lower and upper bounds.

Construct a

99​%

confidence interval about

muμ

if the sample​ size, n, is 35 what is the lower and upper bounds?

Answer 1

a)
sample mean, xbar = 18.4
sample standard deviation, s = 4.9
sample size, n = 35
degrees of freedom, n - 1 = 34

For 95% Confidence level, the t-value = 2.03

CI = (xbar - t*s/sqrt(n), xbar + t*s/sqrt(n))
CI = (18.4 - 2.03 * 4.9/sqrt(35) , 18.4 + 2.03 * 4.9/sqrt(35))
CI = (16.72 , 20.08)

b)
For 99% Confidence level, the t-value = 2.73

CI = (xbar - t*s/sqrt(n), xbar + t*s/sqrt(n))
CI = (18.4 - 2.73 * 4.9/sqrt(35) , 18.4 + 2.73 * 4.9/sqrt(35))
CI = (16.14 , 20.66)