We are studying mutual bond funds for the purpose of investing in several funds. For this

Question

particular study, we want to focus on the assets of a fund and its five-year performance.
The question is: Can the five-year rate of return be estimated based on the assets of the
fund? Nine mutual funds were selected at random, and their assets and rates of return are
shown below.

a. Draw a scatter diagram.
b. Compute the coefficient of correlation.
c. Compute the coefficient of determination.
d. Write a brief report of your findings for parts b and c.
e. Determine the regression equation. Use assets as the independent variable.
f. For a fund with $400.0 million in sales, determine the five-year rate of return (in percent).

Write out the hypotheses (both null and alternate), alpha, test statistic (highlight where it is calculated on your spreadsheet),
decision, conclusion as demonstrated in the odd-problem solution demonstrations


Fund Assets ($mill) Return (%)
AARP High Quality Bond 622.2 10.8
Babson Bond L 160.4 11.3
Compass Capital Fixed Income 275.7 11.4
Galaxy Bond Retail 433.2 9.1
Keystone Custodian B-1 437.9 9.2
MFS Bond A 494.5 11.6
Nichols Income 158.3 9.5
T. Rowe Price Short-term 681 8.2
Thompson Income B 241.3 6.8

Answer 1

Hypotheses:
Null Hypothesis: There is no correlation between the assets of a fund and its five-year rate of return.
Alternate Hypothesis: There is a correlation between the assets of a fund and its five-year rate of return.

Alpha: 0.05

Test Statistic: Pearson's Correlation Coefficient (calculated from the scatter diagram)

Decision: Reject the null hypothesis if the Pearson's Correlation Coefficient is greater than or equal to 0.05.

Conclusion: Based on the Pearson's Correlation Coefficient, we can conclude that there is a correlation between the assets of a fund and its five-year rate of return.