Question (1): A hedge fund analyst who studies market behaviors over lengthy periods of time claims that the equity markets exhibit low volatility. Volatility, on an annual basis, is measured on the level of dispersion of average annual market returns. In other words, volatility is determined by measuring the standard deviation of the average annual returns. The analyst claims that the long run measure of volatility is 4.55%. An investor has acquired twenty-five years of data and has estimated market volatility using the sample standard deviation which was determined to be 6.54%. Annual returns are normally distributed.

(a) At the 5% level of significance, is there any truth regarding the low level of market volatility claimed by the analyst? Explain.

(b) Estimate the p-value and what do you infer from this?

(c) Construct a 95% confidence interval for the true level of market volatility. What is your inference?

(d) Redo the test by adjusting the level of significance to (a) 10% and (b) 1% and what do you infer based on the sample data?

Please send me answer in type form strictly prohibited handwritten solution.