Question

The Wall Street Journal's Shareholder Scoreboard tracks the performance of 1000 major U.S. companies. The performance of each company is rated based on the annual total return, including stock price changes and the reinvestment of dividends. Ratings are assigned by dividing all 1000 companies into five groups from A (top 20%), B (next 20%), to E (bottom 20%). Shown here are the one-year ratings for a sample of 60 of the largest companies.

A. 5
B. 8
C. 15
D. 20
E. 12

a) What is the value of the test statistic?

b) What is the critical value of the test statistic?

c) What is the p-value (or range for the p-value if you are using the tables)

d) What is your decision and conclusion in the context of the problem, i.e., does the data fit the hypothesized distribution or not?

Answer 1

Ans:

	Observed(fo)	Expected(fe)	(fo-fe)^2/fe
A	5	12	4.083
B	8	12	1.333
C	15	12	0.750
D	20	12	5.333
E	12	12	0.000
Total	60	60	11.500

a)Test statistic:

Chi square=11.500

b)df=5-1=4

critical chi square=CHIINV(0.05,4)=9.488

c)p-value=CHIDIST(11.50,4)=0.0215

d)As,p-value<0.05,we reject the null hypothesis and we can conclude that the data does not fit the hypothesized distribution.