Question

A collage register has received numerous complains about the online registration procedure at her collage, alleging that the system is slow, confusing, and error prone. She wants to estimate the proportion of all students at this collage who are dissatisfied with the online registration procedure.

1. What is the most conservative estimates of the sample size that would limit the maximum error to be within 0.05 of the population proportion for a 90% confidence interval
2. Assume that a preliminary study has shown that 70% of the students surveyed at this collage are dissatisfied with the current online registration system. How large a sample should be taken in this case so that the maximum error to be within 0.05 of the population proportion for a 95% confidence interval?

Answer 1

solution:

a)

the given margin of error = E = 0.05

confidence level = 90% = 0.90

= 1-0.90 = 0.10

critical value of z =

we have to find the required sample size, to obain a margin of error of 0.05 for proportion of dissatiesfied

proportion of dissatisfied from online registration process is not given,

so, we assumed = 0.5, to obtain a maximum sample size required

margin of error =

so the required sample size = 271

b)

the given margin of error = E = 0.05

confidence legvel = 95%

= 1-0.95 = 0.05

critical value of z =

proportion of students dissatisfy from the registation process = p = 0.70

so the required sample size = 323