How profitable are different sectors of the stock market? One way to answer such a question is to examine profit as a percentage of stockholder equity. A random sample of 32 retail stocks was studied for x1, profit as a percentage of stockholder equity. The result was x1 = 13.2. A random sample of 33 utility (gas and electric) stocks was studied for x2, profit as a percentage of stockholder equity. The result was x2 = 10.0. Assume ?1 = 4.2 and ?2 = 2.6. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some cases, this choice will increase the P-value by a small amount or increase the length of the confidence interval, thereby making the answer slightly more "conservative." (a) Let ?1 represent the population mean profit as a percentage of stockholder equity for retail stocks, and let ?2 represent the population mean profit as a percentage of stockholder equity for utility stocks. Find a 95% confidence interval for ?1 − ?2. (Round your answers to two decimal places.) lower limit upper limit (b) Test the claim that the profit as a percentage of stockholder equity for retail stocks is higher than that for utility stocks. Use ? = 0.01. (i) What is the level of significance? What is the value of the sample test statistic? (Round your answer to two decimal places.) (iii) Find the P-value. (Round your answer to four decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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How profitable are different sectors of the stock market? One way to answer such a question is to examine profit as a percentage of stockholder equity. A random sample of 32 retail stocks was studied for x₁, profit as a percentage of stockholder equity. The result was

x₁ = 13.2.

A random sample of 33 utility (gas and electric) stocks was studied for x₂, profit as a percentage of stockholder equity. The result was

x₂ = 10.0.

Assume ?₁ = 4.2 and ?₂ = 2.6. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some cases, this choice will increase the P-value by a small amount or increase the length of the confidence interval, thereby making the answer slightly more "conservative."

(a) Let ?₁ represent the population mean profit as a percentage of stockholder equity for retail stocks, and let ?₂ represent the population mean profit as a percentage of stockholder equity for utility stocks. Find a 95% confidence interval for ?₁ − ?₂. (Round your answers to two decimal places.)

lower limit
upper limit

(b) Test the claim that the profit as a percentage of stockholder equity for retail stocks is higher than that for utility stocks. Use ? = 0.01.

(i) What is the level of significance?

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(iii) Find the P-value. (Round your answer to four decimal places.)

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