Question

The following sample data are from a normal population: 9, 7, 11, 14, 12, 10, 5, 4.

(a)

What is the point estimate of the population mean?

(b)

What is the point estimate of the population standard deviation? (Round your answer to three decimal places.)

(c)

With 95% confidence, what is the margin of error for the estimation of the population mean? (Round your answer to one decimal place.)

(d)

What is the 95% confidence interval for the population mean? (Round your answer to one decimal place.)

Answer 1

a)
sample mean, xbar = 9

b)
sample standard deviation, s = 3.464

c)
sample size, n = 8
degrees of freedom, df = n - 1 = 7

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.365

ME = tc * s/sqrt(n)
ME = 2.365 * 3.464/sqrt(8)
ME = 2.9

d)
CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (9 - 2.365 * 3.464/sqrt(8) , 9 + 2.365 * 3.464/sqrt(8))
CI = (6.1 , 11.9)