Question

In a random sample of 5 microwave ovens, the mean repair cost was $75.00 and the standard deviation was $12.50. Construct a 95% C.I. for the population mean. Assume Normality. (Please show your work)

Answer 1

Solution :

Given that,

= 75

s =12.50

n = Degrees of freedom = df = n - 1 =5 - 1 = 4

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,4 = 2.776 ( using student t table)

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

= 2.776 * ( 12.50/ 5)

= 15.5

The 95% confidence interval mean is,

- E < < + E

75 - 15.5 < <75+ 15.5

59.5 < < 90.5