Question

A sample of size n =52 is drawn from a normal population whose standard deviation is σ=7.9. The sample mean is x=43.78

(a) Construct a 80% confidence interval for μ. Round the answer to at least two decimal places..

(b) If the population were not approximately normal, would the confidence interval constructed in part (a) be valid? Is the sample large?

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 43.78

Population standard deviation =    = 7.9

Sample size n =52

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.10

Z/2 = Z0.10= 1.28 ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.28 * ( 7.9/  52 )

= 1.40
At 80% confidence interval estimate of the population mean
is,

- E < < + E

43.78- 1.40 <   < 43.78 + 1.40

42.38 <   < 45.18

( 42.38 , 45.18)

If the population were not approximately normal, than not confidence interval constructed