Question

A random sample of 30 Suffolk University employees had an average commute length of 13.5 miles, with a standard deviation of 7.5 miles. What is the 90% confidence interval for the mean commute length of all Suffolk employees? Use 4 non-zero decimal places in your calculations.

(a) Find the tα/2 , df

(b) Find σx

(c) Find the margin of error (MoE) and construct the confidence interval

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 13.5

sample standard deviation = s = 7.5

sample size = n = 30

Degrees of freedom = df = n - 1 = 30 - 1 = 29

a) At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t0.05,29 = 1.699

b) s = s / n = 7.5 / 30 = 1.3693

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

= 1.699 * 1.3693

Margin of error = E = 2.33

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

  ± E  

= 13.5   ± 2.33

= ( 11.17, 15.83 )