Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.
Show your work

n = 30, x bar = 89.3, s = 18.9, 90 percent

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 89.3

sample standard deviation = s = 18.9

sample size = n = 30

Degrees of freedom = df = n - 1 =30-1=39

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,29 = 1.700

Margin of error = E = t/2,df * (s /n)

= 1.700 * (18.9 / 30)

Margin of error = E = 5.9

The 90% confidence interval estimate of the population mean is,

- E < < + E

89.3 - 5.9 < < 89.3 + 5.9

83.4 < < 95.2

(83.4,95.2)