Question

NT1 Price/earnings ratios have been obtained for a random sample of 10 NYSE stocks selected on a particular day. The mean ratio is 32.3. Assume that σ = 10 and that price/earnings ratios for NYSE stocks are normally distributed. Construct an 80% confidence interval for the true mean price/earnings ratio for all NYSE stocks.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 32.3

Population standard deviation = = 10

Sample size = n = 10

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

Z_/2 = Z_0.10 = 1.28

Margin of error = E = Z_/2* ( /n)

= 1.28 * (10 / 10)

= 4.05

At 80% confidence interval estimate of the population mean is,

- E < < + E

32.3 - 4.05 < < 32.3 + 4.05

28.25 < < 36.35

(28.25 , 36.35)