Hypothesis Testing of Population Variance Homework Problems 1) The standard deviation of daily returns of a stock's price is used as a measure of the

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Hypothesis Testing of Population Variance Homework Problems 1) The standard deviation of daily returns of a stock's price is used as a measure of the risk of that stock. Suppose that in a sample of 101 days, the standard deviation of a particular stock is 1.15%. a) Find the 90% confidence interval of the population variance for this stock. b) In the past, the standard deviation of the daily returns of this stock has been 1.56%. Test the hypothesis at the 1% level of significance that the standard deviation has decreased from its previous level. 2) A mutual fund has provided the following returns in each of the previous 5 years: 12.3, 14.5, 18.9, 6.5, and 9.8. If we use the standard deviation of returns as a measure of risk (with a larger standard deviation indicating more risk) a) find the sample standard deviation of returns of this mutual fund Population Variance Homework Problems 1 b) what is the 95% confidence interval for the population standard deviation measure of risk for this mutual fund? 3) The US Tennis Association is considering switching the type of tennis ball used for it tournament events. For a brand of balls to be \"acceptable\" to the USTA, when dropped from a certain height, the balls must bounce an average of at least 4 feet. The USTA is reasonable happy with the current balls they use, but would be willing to switch to a new brand if they were confident that the new brand of balls were more consistent (had a lower variance) compared to the current balls they use. The standard deviation of the heights the current brand of balls bounced when dropped used is .48 feet. In a sample of 91 balls from the new brand being tested, the sample standard deviation is .38 feet. At the 5% level of significance, is there enough evidence that the new balls are more consistent (have a lower variance) than the current brand? Population Variance Homework Problems 2 4) Two methods of filling cereal boxes are being compared. Both methods fill the box with the same amount of cereal on average so the company wants to select the method with the lower variance. In a sample of 31 boxes filled using method 1, the standard deviation of fill weights is .75 ounces and in a sample of 41 boxes filled using method 2, the standard deviation is .65 ounces. At the 5% level of significance, does it appear that the variance of method 1 is significantly larger than the variance of method 2? 5) An investor is trying to decide between 2 mutual funds. Mutual fund #1 offers a slightly higher return than mutual fund #2 so the investor decides that he will invest in mutual fund #1 unless the risk of mutual fund #1 is significantly higher than the risk of mutual fund #2. Using the standard deviation of 101 daily returns as a measure of risk of the two mutual funds, the investor finds that the standard deviation of mutual fund #1's daily returns is .95 and the standard deviation of mutual fund #2's daily returns is .81. At the 10% level of significance, should the investor invest in mutual fund #1 or #2? 6) A machine makes drill bits. When the machine is operating correctly, the variance of the diameter of drill bits is no more than .04 inches. In a random sample of 81 drill bits, the sample variance was .07. Test the hypothesis at the 1% level that the machine is operating correctly. Population Variance Homework Problems 3 7) Two different brands of milk are randomly samples, and the fat content in each bottle of mild is determined. Twenty six bottles of Brand A yielded an average fat content of 26 grams with a standard deviation of 5 grams, and 31 bottles of Brand B yielded an average fat content of 25.8 grams with a standard deviation of 7 grams. Test the hypothesis at the 10% level of significance that the variances are different. Population Variance Homework Problems 4