An investor with a stock portfolio sued his broker, claiming that a lack of diversification in his portfolio had led to poor performance. The data, shown below, are the rates of return (percent) of the portfolio for the 39 months that the account was managed by the broker. (The data are in chronological order, reading the table row-wise.)

The arbitration panel used the average of the "Standard and Poor's 500 stock index" for the same period, which was 0.95%, as a reference performance. Consider the 39 monthly rates of return as a random sample from the population of monthly rates of return the  brokerage would generate if it managed the account forever.

Reference: Moore, D.S., McCabe, G.P., and Craig, B. (2008), Introduction to the Practice of Statistics, 6th edition (New York: Freeman)

Investigate whether there is evidence that the brokerage in its handling of this account yields an average monthly rate of return different from the reference performance.

1. State the model behind the appropriate t-test, and assess those assumptions for which sufficient information has been provided. (You are given that your assessment will not reveal any problems with the model and that the t-test is appropriate.)

2. Clearly state the appropriate null hypothesis and carry out the t-test

3. If it is concluded that there is evidence of an average monthly rate of return different from the reference performance, obtain a 95% confidence interval for this difference. Explain in your own words how the confidence interval should be interpreted

4. Synthesise your investigations into a coherent report, incorporating each part above and any further discussion as appropriate + A note of caution. In your use of the relevant procedure in the statistical computing software, ensure that you enter the appropriate Null hypothesis: µ = value