Question

1.6448
An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 90% confidence interval for the proportion who are not satisfied.

(a) Past studies suggest that this proportion will be about 0.29. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.025.
(You will need a critical value accurate to at least 4 decimal places.)
Sample size: to 4 decimal places!

Answer 1

Proportion, p =0.29

Let n be sample size.

So, standard deviation of p =

=0.1

So margin of error = Z/2=0.05 *standard deviation of p or, 0.025=1.6449*

or, 0.0152=

or, 0.000231=0.29*0.71/n

or, n= 891.3420

So, sample size would be 891.3420.

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