Question

In a random sample of 40 dog owners enrolled in obedience training, it was determined that the mean amount of money spent per owner was $107.89 per class with a standard deviation of $8.20. Construct and interpret a 95% confidence interval for the mean amount spent per owner for an obedience class.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 107.89

Population standard deviation =    =8.20

Sample size n =40

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
=1.96 * ( 8.20 / 40 )

= 2.50
At 95% confidence interval mean
is,

- E < < + E

107.89- 2.50 <   < 107.89+ 2.50

105.39 <   < 110.39

(105.39 ,110.39)