normally distributed

Question

A certain brokerage house wants to estimate the mean daily return on a certain stock. A random sample of 9 days yields the following return percentages.

-1.6, -2.35, -2.3, 1.79, 1.01, -0.82, -2.66, 0.74, 2.27

If we assume that the returns are normally distributed, find a 90% confidence interval for the mean daily return on this stock. Give the lower limit and upper limit of the 90% confidence interval.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

Lower limit:

Upper limit:

Answer 1

We are told that returns are normally distributed and we want a 90% confidence interval for a population mean. We don't know the population standard deviation, so we will use a t confidence interval.

Formula:

From your data,

x-bar = -0.436, s = 1.915, n = 9

The t critical value for 90% confidence and df = n-1 = 9-1 = 8 can be found on a t-table. Look at tail area = 0.05 (90% confidence means an area of 0.9 in the middle and an area of 0.05 in each of the tails).

t critical value = 1.860

Plugging this all into the formula, we get