Question

A report in a research journal states that the average weight loss of people on a certain drug is 17 lbs with a margin of error of ±5 lbs with confidence level C = 95%.

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

(b) If the study is repeated, how large should the sample size be so that the margin of error would be less than 2.5 lbs? (Assume ?= 5 lbs.)
ANSWER:  

Answer 1

Solution,

Given that,

a) $\bar x$ = 17

E = 5

At 90% confidence interval estimate of the population mean low is,

$\bar x$ - E

= 17 - 5 = 12

b) Given that,

Population standard deviation = $\sigma$ = 5

Margin of error = E = 2.5

At 95% confidence level the z is,

$\alpha$ = 1 - 95%

$\alpha$ = 1 - 0.95 = 0.05

$\alpha$/2 = 0.025

Z_$\alpha$/2 = 1.96

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = [ 1.96 * 5 / 2.5]²

n = 15.37

Sample size = n = 16