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# Probablitiles, Confidence intervals, Hyothesis testing

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Using Excel, assume that the distribution of the population of all stocks on that index is normal, and using the mean and standard deviation from your sample as point estimates, find the following probabilities:
P (a price is greater than \$20)
P (a price is less than \$90)
P (a price is between \$30 and \$40)

Determine the actual percentage of your sample stocks in Sample "A" that were greater than \$20, less than \$90, and between \$30 and \$40 by counting the number. Give reasons why these percentages may differ from those found in Part I above.

Using Sample "A" construct, explain and interpret a 90% confidence interval for the mean of all stocks in your index.
Using Sample "A" construct, explain and interpret a 95% confidence interval for the mean of all stocks in the index based on your sample of 50 stocks.

Conduct a test of the hypothesis that the mean price (current) of the stocks on Sample "A" is the same as the mean price (current) of all of the stocks in Sample "B." Show all five steps.

Discuss the implications of the results of this hypothesis test. In this discussion, reference the current value of each index.

Use the Sample "A" 50 stocks with the current price and the price for one year ago to conduct a paired test to determine if there has been a significant change in these stock values in the last year. Compute the mean change as a percent and compute the mean change in the index for the two dates. Explain your results.

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