Question

A report in a research journal states that the average weight loss of people on a certain drug is 16 lbs with a margin of error of ±3 lbs with confidence level C = 95%. (a) According to this information, the mean weight loss of people on this drug, ?, could be as low as 16 lbs. (b) If the study is repeated, how large should the sample size be so that the margin of error would be less than 1.5 lbs? (Assume ?= 5 lbs.)

Answer 1

Given that the average weight loss of people on a certain drug is M = 16 lbs with a margin of error of E = ±3 lbs with confidence level C = 95%.

So, the confidence level is concluded as:

CI = M ± E

thus CI = {16 ±3 }

The lower limit of the interval will be 13 and

The upper limit will be 19.

a)So, According to this information, the mean weight loss of people on this drug, ?, could be as low as 13 lbs.

b) If the margin of error is assumed as E = 1.5 and the population standard deviation as ?= 5 lbs.

The Minimum sample is calculated as:

Where Zc is the critical standard score which is calculated using excel formula for norma distribution which is =NORM.S.INV(0.975) thus Zc = 1.96

now the minimum sample is computed as: