Mathematics
Sample Size Considerations

Question Description

Final Answer

For an 80% confidence interval, we would have a critical z value of

z_crit = norm.inv(0.9,0,1) = 1.281551566

The margin of error for the confidence interval will be z_crit x SEM

So 2.5 = 1.281551566 x sd/sqrt(n)

2.5 x sqrt(n) = 1.281551566 x sd

sqrt(n) = 1.281551566 x 5/2.5

n = 6.57


So, naively, we could say that the minimum required sample size is 7. In practice, we should take into account that we would be using the t-distribution, which would certainly increase the required sample size to 8-9, but since the degrees of freedom are dependent on n I'm not sure this is really what the example wants you to address (since it gets quite complex, mathematically).

iainharlow (1041)
Duke University

Anonymous
Solid work, thanks.

Anonymous
The tutor was great. I’m satisfied with the service.

Anonymous
Goes above and beyond expectations !

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors