Question

In a study, we see that the average number of close confidants in a random sample of 2006 US adults is 2.2 with a standard deviation of 1.4 . If we want to estimate the number of close confidants with a margin of error within and with 90% confidence, how large a sample is needed? R

Answer 1

527

Explanation:

Data provided in the question:

standard deviation, s = 1.4

Confidence level = 90%

Margin of error, E = 100% - 90% = 10% = 0.10

Now,

For 90% confidence level , the z value is = 1.64

also,

the relation for sample size and above data is given as

Sample size, n = [(z × s) ÷ E]²

or

n = [(1.64 × 1.4 ) ÷ 0.10]²

or

n = 527.16 ≈ 527