A study of the trading skills of institutional investors-the men and women who t

Question

A study of the trading skills of institutional investors-the men and women who
trade stocks for pension funds and similar institutional holdings-was carried out to
see if these people were better or worse at trading stocks of three categories: Growth
Stocks, Value Stocks, and Past Losers. The total sample size was n= 3,816 stocks and
the computed ,Fstatistic value was 1.17.
a. State the null and alternative hypotheses.
b. What are the degrees of freedom for error?
c. What are the degrees of freedom for "factor"?
d. What are the degrees of freedom for "total"?
e. Carry out the test and state your conclusions, including an estimated p-value.
f. Write a short report to the management of a pension fund describing your
findings and explaining whether or not there is statistical evidence that
institutional traders are better or worse at trading stocks in one of the three
groups of stock under study as compared with those in the other two.

Explanation / Answer

Solution:-

a)

n = 3816, k = 3

Null hypothesis, H0: 1 = 2 = 3

Alternate hypothesis, H1: Means are not all equal.

b) The degrees of freedom for error = c - 1 = 2

c) The degrees of freedom for "factor" = n - c = 3816 - 3 = 3813

d) The degrees of freedom for "total" = n - 1 = 3813 - 1 = 3812

e) The test and state your conclusions, including an estimated p-value

Significance value = 0.05

F statistics:-

F = 1.17

p value = 0.310478

Since p-value(0.3105) is more than significance value(0.05) so we cannot reject the null hypothesis.

From this we can conclude that we have sufficient evidence that sample mean of all the three stocks are same.

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