Question

Section 8.1 #38

A sample of size n = 80 is drawn from a normal population whose standard deviation is σ = 6.8. The sample mean is x̄ = 40.41.

a.	Construct a 90% confidence interval for μ.
b.	If the population were not approximately normal, would the confidence interval constructed in part (a) be valid? Explain

Answer 1

Solution :

(a)

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z 0.05 = 1.645

Margin of error = E = Z/2* ( /n)

= 1.645 * (6.8 / 80)

= 1.25

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

- E < < + E

40.41 - 1.25 < < 40.41 + 1.25

39.16 < < 41.66

(39.16 , 41.66)

(b)

The confidence interval constructed in part (a) is not valid because we must need

  the population were approximately normal .