Question

III. The average population earnings per share for financial service corporations, such as American Express, E * Trade Group, Goldman Sachs and Merril Lynch, were $ 3 (Business Week, August 14, 2000). In 2001, the following earnings data per share was obtained for a sample of 10 financial services corporations:

1.92
2.16
3.63
3.16
4.02
3.14
2.20
2.34
3.05
2.38

Perform the analysis required to determine if the average population earnings per share in 2001 differ from the three dollars reported in 2000, with a 5.0% margin of error.

Answer 1

Consider X be the random variable denoting the earnings of the financial services.

Here X follows normal distribution , since the sample size is small and population standard deviation is unknown so  t distribution will use with n-1=10-1=9 degrees of freedom.

The sample mean is given by

ΣΧ Χ-

=28/10=2.8

The sample standard deviation is given by

=0.7

Σχ2 (nX2) п — 1 ΣΧ-

Hypothesis can be written as:

The null hypothesis be that mean average earnings is equal to $3.

The alternate hypothesis be that mean average earnings is not equal to $3.

Ho:$\mu$=3 vs H1:$\mu \neq$3

TEST STATISTICS IS GIVEN BY

т — P tn-1,a Уп n

substituting the values test statistics obtained is -0.903.

The t-critical at 5% margin of error with 9 degree of freedom form the t value table is 1.833.

The test statistic is less than 5% critical value which is 1.833.

So, the null hypothesis is accepted and it can be concluded that the mean average earing is equal to $3.