Smith manages a portfolio of stocks. He picks a set of stocks at the beginning of a year and holds them until the end of the year. An important measure of Smith's performance is the proportion of stocks in his portfolio that rose in value over the year. For the most recent year, of the 52 stocks in his portfolio, 40 stocks rose in value.

In the broad universe of stocks from which Smith selects his portfolio, 76% of the stocks rose in value.

a. What percentage of his stocks rose in value? (Write up to two decimal places; for example, [70.01]%)

[ ]%

b. We wish to test if Smith's performance shows evidence of a statistically significant ability to pick stocks based on the measure described above.

i) Define the parameter to be tested.

ii) State the null and the alternative hypotheses. Write out your test in terms of the parameter define in part (i).

iii) State type I and type II errors in plain English in the context of the problem.

iv) Use StatTools to conduct the hypothesis test. Generate the StatTools report, and copy and paste the screenshot of your report (including your name and report created data and time on top of the report) in the answer box.

Note: Do not attach your Excel file. Points will be deducted if you attach your Excel file instead of providing the screenshot of the StatTools repot. To insert your repot, save your screenshot as a graphic (png) file, and then Insert->Image->Upload Image.

v) At the 10% level of significance, does Smith's performance show a statistically significant ability to pick stocks? Explain your answer.