Past experience indicates that the breaking strength of yarn

Past experience indicates that the breaking strength of yarn used in manufacturing drapery material is normally distributed and that = 2 psi. A random sample of 15 specimens is tested and the average breaking strength is found to be ¯x = 97.5 psi.

(a) Find a 95% confidence interval on the true mean breaking strength.

(b) Find a 99% confidence interval on the true mean breaking strength.

Please show step by step, Thank You

Solution

a.
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=97.5
Standard deviation( sd )=2
Sample Size(n)=15
Confidence Interval = [ 97.5 ± Z a/2 ( 2/ Sqrt ( 15) ) ]
= [ 97.5 - 1.96 * (0.516) , 97.5 + 1.96 * (0.516) ]
= [ 96.488,98.512 ]
b.
WHEN Z=99%
Confidence Interval = [ 97.5 ± Z a/2 ( 2/ Sqrt ( 15) ) ]
= [ 97.5 - 2.58 * (0.516) , 97.5 + 2.58 * (0.516) ]
= [ 96.168,98.832 ]