Question

Suppose you have been following a particular airline stock for many years. You are interested in determining the average daily price of this stock in a 10-year period and you have access to the stock reports for these years. However, you do not want to average all the daily prices over 10 years because there are several thousand data points, so you decide to take a random sample of the daily prices and estimate the average. You want to be 90% confident of your results, you want the estimate to be within $3.00 of the true average, and you believe the standard deviation of the price of this stock is about $13.25 over this period of time. How large a sample should you take?

Answer 1

Solution :

Given that,

Population standard deviation = = 13.25

Margin of error = E = 3.00

At 90% confidence level the z is,

= 1 - 90%

= 1 - 0.90 = 0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

sample size = n = [Z/2* / E] 2

n = [1.645 * 13.25 / 3.00]2

n = 52.78

Sample size = n = 53