Q.5 Sara is a stockbroker and psychic.  She claims that she provides clients with stock market advice which is in good harmony with a client's "aura" and "karma" and which is attuned to the client's own personal astrological chart.  Daniela is a bit wary of these claims, but decides to invest with Sara for a trial period of one year.  She purchases five stocks, on Sara's advice.  At the end of the year Daniela checks to see whether she could on an average depend on Sarah's psychic abilities for investment decisions.

(a) State the null and alternative hypotheses, in words and in symbols.

(b) The five stocks that Sara recommended to Daniela had returns of +10%, -15%, +5%, +30%, and -5% over the one-year trial period.  (The overall stock market, as measured by the S&P 500, lost 6% over the course of that year.)

Compute the test statistic.Explain the choice of your test statistic. Use α = 0.05. Give the p-value.

(c) Based on your calculations do you think Sara hasinvesting abilities based on her being a psychic?

(d) What would be a Type I error in this scenario?