Question

a. A previous study of nickels showed that the the standard deviation of the weight of nickels is 300 milligrams. A coin counter manufacturer wishes to find the 99% confidence interval for the average weight of a nickel. How many nickels does he need to weigh to be accurate within 10 milligrams?

900

5972

8595

4871

b. A researcher conducted a study of the access speed of 30 hard drives and concluded that his maximum error of estimate was 20. If he were to conduct a second study to reduce the maximum error of estimate to 5, about how many hard drives should he include in his new sample?

30

60

120

480

Answer 1

a)

Solution :

Given that,

Z_/2 = 2.576

sample size = n = [Z_/2* / E] ²

n = [2.576 * 300 / 10]²

n = 5972

Sample size = n = 5972

b)

Generally, the rule is to reduce the error by a factor of 2, you need 2² = 4 times the sample size;

here you want to reduce the error by a factor of 4 (from 20 to 5), so you would need to ((2²)² )=16 times the sample size

So, 16 * 30 = 480

New sample = 480