Question

#1.Construct a 95% confidence interval to estimate the

population mean using the following data:
sample mean = 75
sample standard deviation = 20
sample size = 36
#2.What is the margin of error?
#3.You

Answer 1

#1 The 95% confidence interval for estimation of the population mean comes out to be,

u = 75 ± 6.533

I.e. the population mean is between 68.487 and 81.533 (with 95% confidence)

#2 margin of error = 6.533

Explanation:

Mean = M = 75

Standard Deviation = S = 20

Sample Size = n = 36

95% confidence interval,

this corresponds to an alpha value of 0.025

This corresponds to the Z value of,

Z = 1.96

Now,

finding the estimate for the population mean, we use the formula,

Population Mean = u = m ± ZS/√n

Putting in the values,

u = 75 ± (1.96)(20)/(√36)

u = 75 ± 6.533

This is the estimate for the population mean with a margin of error of ±6.533