Question

In a sample of 1000 randomly selected consumers who had opportunities to send in a rebate claim form after purchasing a product, 240 of these people said they never did so. Reasons cited for their behavior included too many steps in the process, amount too small, missed deadline, fear of being placed on a mailing list, lost receipt, and doubts about receiving the money.

Calculate an upper confidence bound at the 95% confidence level for the true proportion of such consumers who never apply for a rebate. (Round your answer to four decimal places.)

Answer 1

Solution :

Given that,

n = 1000

x =240

Point estimate = sample proportion = = x / n = 240 /1000=0.24

1 - = 1 - 0.24=0.76

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

=0.05
Z= Z_{0.05 = 1.645} Using z table  

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 (((0.24*0.76) /1000 )

E= 0.0222

A 95% confidence interval for population proportion p is ,

+ E

0.24 +0.0222

0.2622

upper bound=0.2622