Construct a 95% confidence interval for the population mean given the following

Question

Construct a 95% confidence interval for the population mean given the following: sample mean = 16, population standard deviation = 1.5 and sample size = 49.

Answer 1

mean + and - z(sd)/sqrn

for 95% z = about 2, using the empirical rule

sd=1.5, n=49

16+ and -2(1.5)/7

16 + and - 3/7

the confidence interval is (15 4/7, 16 3/7) = (15.57, 16.43)

more accurately z=1.96 using z tables or a z calculator

16 + and - (1.96)(1.5)/7

(15.58, 16.42)