MATH 137 Project 4 Name:__________________________ Financial data for the rates of return of two stocks A and B for 4 years is as per table. year A B Probability 1 0.4 0.8 0.25 2 0.7 1.2 0.25 3 -0.5 -0.6 0.25 4 0.6 1.0 0.25 A portfolio of the two stocks puts equal amount of money in A and B. 1. Find the covariance of A and B. _____________ 2. Find the expected value of the portfolio rate of return. _____________ Find the standard deviation of the portfolio rate of return ______________ Find the Sharpe Ratio; that is the ratio of the expected value to the standard deviation. ______________ A random sample of 225 exams score drawn from a large population of students has a mean of 60 and a sample standard deviation of 9. 3. Estimate the population mean with a confidence level of 95%. _______< Estimate the population mean with a confidence level of 98%. _______ < <________ <________ Your final answers should be correct to 4 places after the decimal point. 4. For a confidence level of 95% assuming the same statistics find the sample size that would result in a margin of error of 1.5. ______________ For a sample size of 225 find the level of confidence that would result in a margin of error of 1.5. ________________ Your final answers should be correct to 3 places after the decimal point. 5. A poll of 100 voters shows that 66 of them would vote for Boris for Treasurer of Betropolis. Estimate the proportion of votes that he would get from the population with a confidence level of 95%. ___________ Estimate the proportion of votes that he would get from the population with a confidence level of 90%. __________ Your final answers should be correct to 3 places after the decimal point. 6. The ages of seniors at Betropolis University are not Normally distributed. A random sample of 24 students has a sample mean of 22 and a sample standard deviation of 2.3 years. Estimate the population mean for a 95% confidence level. Your final answers should be correct to 2 places after the decimal point. The estimate of population mean: __________< < ____________ You must use the T - distribution. Betropolis conducts an advertising campaign to get people to lose weight. A random sample of 49 people results in an average loss of 1.5 pounds with a sample standard deviation of 7 pounds. Can we infer that the campaign had an effect (good or bad) as opposed to no effect? 7. Test (2-tailed) the (alternative) hypothesis at a confidence level of 95%. Estimate of population mean:________< <________. Reject or accept ? _______ H0 Now test the hypothesis at a confidence level of 60%. Estimate of population mean: _______< < _______. Reject or accept ?_______ H0 Your final answers should be correct to 3 places after the decimal point. 8. Determine whether the following statements are true (T) or false (F). a. ____ Newton discovered the Normal Distribution. b. _____ The Normal distribution is symmetric. c. ______ As sample size increases the T-distribution approaches the Normal distribution. d. _____ The Central Limit Theorem allows us to use the the properties of the Sample Mean Random variable to infer information abot the population mean. e. _____ The greater the confidence level the harder it is to reject the Null Hypothesis. f. _____ When estimating population proportion a large sample size results in a less accurate estimate. g. ______ The Margin of Error is found by using the sample mean. h. _______ The greater the sample size the greater the Margin of Error. i. ______The covariance of A with A is 0. j. ______ If X versus Y is linear then the correlation is 0. 9. Fill in the appropriate phrase or number. a. b. is called the _____________hypothesis HA (X ) ___ c. X and Y independent Cov ( X , Y ) ___ d. ( X ) ___ e. ____< <_____ 2