Answer:
a. (29526.192 , 32155.808)
b. (29673.9301 , 32008.0699)
Step-by-step explanation:
on calculation, we find that sample mean = 30843 and sample standard deviation = 3018.504, and n=20
1)
Sample Mean = 30841
SD = 3000
Sample Size (n) = 20
Standard Error (SE) = SD/root(n) = 670.8204
alpha (a) = 1 - 0.95 = 0.05
z critical value for 95% confidence interval:
z(a/2) = z(0.025) = 1.96
Margin of Error (ME) = z(a/2) x SE = 1314.808
95% confidence interval is given by:
Sample Mean +/- (Margin of Error) = 30841 +/- 1314.808
= (29526.192 , 32155.808)
2)when std dev of population is not known, we use sample's, but we have to use t instead of z
Sample Mean = 30841
SD = 3018.504
Sample Size (n) = 20
Standard Error (SE) = SD/root(n) = 674.958
alpha (a) = 1-0.9 = 0.1
we use t-distribution as population standard deviation is unknown
t(a/2, n-1 ) = 1.7291
Margin of Error (ME) = t(a/2,n-1)x SE = 1167.0699
90% confidence interval is given by:
Sample Mean +/- (Margin of Error)
30841 +/- 1167.0699 = (29673.9301 , 32008.0699)
