Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread wear was found to be 50,000 miles with a standard deviation of 3,500 miles. What is the best estimate of the average tread life in miles for the entire population of these tires?
Answer(s): D
The sample mean is a good estimate of the population mean.
You have a portfolio of two assets, X and Y. X has an expected return of 15% with a variance of 900%%, and Y has an expected return of 9% with a variance of 400%%. Assume the covariance between X and Y is 225%%. For a portfolio composed of 50% X and 50% Y, find the expected return and variance.
Answer(s): B
The expected return is 0.5*15% + 0.5*9% = 7.5% + 4.5% = 12%. The variance will be trickier. The variance will be equal to (w_X)^2 * (sigma_X)^2 + (w_Y)^2 * (sigma_Y)^2 + 2 * w_X * w_Y * cov(X,Y) = (0.5)^2 * 900%% + (0.5)^2 * 400%% + 2 * (0.5) * (0.5) * 225%% = 437.5%%.
How much must you deposit today if you wish to have $20,000 in 10 years, assuming that interest accumulates at 9% per year, compounded annually?
Answer(s): C
On the BAII Plus, press 10 N, 9 I/Y, 0 PMT, 20000 FV, CPT PV. On the HP12C, press 10 n, 9 i, 0 PMT, 20000 FV, PV. Note that the answer is displayed as a negative number. Make sure that the BAII Plus has the P/Y value set to 1.
What is another name for the alternate hypothesis?
The alternate is also referred to as the research hypothesis.
William Henry, a quantitative analyst with Smith, Kleen & Beetchnutty Brokerage, is examining a data sample and has amassed the following information:Standard deviation of the sample: 0.97Number of observations: 109Degrees of freedom: 2Sample mean: 11.03Assume that Mr. Henry formulates a null hypothesis that states that the value of the population mean is equal to zero. Additionally, assume that the population standard deviation is unknown. Given this information, what is the standard error of the estimate? Further, what is the test statistic? Choose the best answer.
If the population standard deviation is unknown, as in this example, the standard error of the estimate is found by using the following equation:{Standard error = s / square root of n} where s = the sample standard deviation and n = the number of observations in the sample.In this example, all of the necessary information has been provided, and the determination of the standard error of the estimate is found as:{Standard error = [0.97 / 10.44] = 0.0929}Now that the standard error of the estimate has been calculated, the test statistic can be found by using the following equation:{Test statistic = [sample statistic - value of the population parameter under the null hypothesis] / standard error of the sample statistic].Again, all of the necessary information has been provided, and the calculation of the test statistic is found as follows:{Test statistic = [11.03 - 0.00] / 0.0929 = 118.73}This is a very large value for the test statistic. In this example, the null hypothesis would likely be rejected unless a very low confidence level is assumed.
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