Ann manages a portfolio of stocks. She picks a set of stocks at the beginning of a year and holds them until the end of the year. An important measure of Ann's performance is the proportion of stocks in her portfolio that rose in value over the year. For the most recent year, of the 50 stocks in her portfolio, 40 stocks rose in value and only 10 stocks declined in value.

In the broad universe of stocks from which Ann selects her portfolio, 75% of the stocks rose in value and 25% declined in value. We wish to test if Ann's performance shows evidence of a statistically significant ability to pick stocks based on the measure described above.

(a)State the null and the alternative hypotheses. Define your parameter and write out your test in terms of the parameter.

(b)Use StatTools to conduct the hypothesis test. Generate the StatTools report, and copy and paste it in the answer box.

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

(d)Provide the interpretation of the p-value in English.