Question

one can calculate the 95% confidence interval for the mean with the population standard deviation knowing this gives us an upper and lower confidence limit what happens if we decide to calculate the 99% confidence interval describe how the increase in the confidence level has changed the width of the confidence interval

Answer 1

I HOPE ITS HELPFUL TO YOU IF YOU HAVE ANY DOUBTS PLS COMMENTS BELOW..I WILL BE THERE TO HELP YOU...ALL THE BEST...

ANSWER:

For 95% confidence:

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    100          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
s = sample standard deviation =    30          
n = sample size =    50          
              
Thus,              
              
Lower bound =    91.68457705          
Upper bound =    108.3154229          
              
Thus, the confidence interval is              
              
(   91.68457705   ,   108.3154229   ) [ANSWER]

***********************

For a 99% confidence:

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    100          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    30          
n = sample size =    50          
              
Thus,              
              
Lower bound =    89.07168179          
Upper bound =    110.9283182          
              
Thus, the confidence interval is              
              
(   89.07168179   ,   110.9283182   ) [ANSWER]

*******************

As we can see, the 99% confidence interval is WIDER than that of 95%.

HOPE YOU UNDERSTAND...

PLS RATE THUMBS UP....ITS HELPS ME ALOT...

THANK YOU...!!