use the given confidence level and sample data to find A the

use the given confidence level and sample data to find A the margin of error and B the confidence interval for the population mean u. Assume that the population has a normal distribution.

weight lost on a diet 90% confidence; n=20, x=6.0kg, s=8.3 kg

Solution

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=6
Standard deviation( sd )=8.3
Sample Size(n)=20
Confidence Interval = [ 6 ± t a/2 ( 8.3/ Sqrt ( 20) ) ]
= [ 6 - 1.7291 * (1.86) , 6 + 1.7291 * (1.86) ]
= [ 2.79,9.21 ]