## Construct confidence interval for the true mean return, Basic Statistics

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A researcher has gathered data on the daily returns on a portfolio of call options over a recent 250-day period. The mean daily return has been 0.001 and the sample standard deviation of daily portfolio returns is 0.0025. The researcher believes that the mean daily portfolio return is not equal to zero.

a) Construct a hypothesis test of the researchers belief at the 5% level of significance.

b) The researcher now wishes to test his belief that the mean daily return is strictly positive. Construct a hypothesis test of this belief at the 5% level of significance.

c) Construct a 95% confidence interval for the true mean return.

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