Statistical tests

1. For all variables, provide the descriptive statistics (no charts or graphs). Then, provide a 95% interval estimate for each variable, using the proper technique for each type of variable.

2. Conduct the appropriate statistical test using data to answer the following:
You would like a new mutual fund, so you study the data to examine the relationship between fund type and net asset value (NAV). Specifically, you would like to determine if fund type affects NAV.

a. What statistical test will you need here?
b. What would be the null and alternative hypotheses?
c. What is the independent and dependent variable?
d. Based on this sample, is there sufficient evidence to conclude that there is a true association between fund type and net asset value? Use 5% significance. State your results correctly.
e. What is the specific effect(s), if any, of fund type on net asset value?
f. What is your conclusion?
g. Does your statistical test meet the required assumptions of the method you used?

3. Conduct the appropriate test and data analysis to determine the association, if any, between 5-year average return and Morningstar ranking. Do any recoding necessary to enable use of the correct statistical test. Does 5-year average have an affect on ranking?

a. What statistical test would you use here?
b. What are the null and alternative hypotheses?
c. What is the independent and dependent variable?
d. Using 5% significance, is Morningstar ranking affected by 5-year average return? State your results in the correct format.
e. Include appropriate visuals to show the specific effect, if any. Interpret the visuals with a brief summary.
f. Briefly discuss your findings. What is your overall conclusion? Write a short paragraph. Be sure to explain your results whether or not significant.
4. Create a predictive model capable of forecasting net asset valuewith expense ratio.

a. What is the IV and DV?
b. What is the % of explained variability? Do any outliers affect it?
c. Is the model statistically significant? State results in the correct format. If significant, what does that result mean about your population?

d. What equation can be used to predict net asset valuewith expense ratio?

e. If a particular fund has an expense ratio of .9, what is the predicted net asset value? Use 95% confidence.
f. Given an expense ratio of .75, estimate the average net asset value for all funds with an expense ratio of .75. Use 95% confidence.
g. Include the appropriate plot to show extreme cases. What do you note? Discuss briefly.
h. Is this model appropriate for net asset value? Support your answer with a short paragraph.

5. Create a predictive model capable of forecasting 5-year average return with expense ratio, net asset value, and Morningstar rank. Morningstar rank should be recoded into an indicator variable. (2 and 3 star ranks should be 0, 4 and 5 star ranks should be 1).

a. What is your % of explained variability?
b. What equation, using all variables, can predict 5-year average return?
c. Your fund has a star ranking of 4, a net asset value of 68.11, and an expense ratio of .63. Estimate your 5-year average returnwith 95% confidence.
d. What is your estimate of the mean 5-year average return for all funds as described in part c? Use 95% confidence.
e. Check the significance of each individual variable on this model. Report results in the appropriate format.
f. Is this model significant overall?
g. Remove any insignificant variables, stepwise, and fully correct the model.
i. New equation?
ii. Explained variability?
iii. Overall significance?
h. On the new model (after stepwise), do you suspect any problems due to collinearity? Support your answer, yes or no.