You are examining a group of 6 stocks. Their average annual standard deviations have been 25%, 20%, 15%, 25%, 16%, and 45%. What is the range of annual standard deviations?
Answer(s): C
The range = the maximum value - the minimum value. Here, we have 45% - 15% = 30%.
Routine physical examinations are conducted annually as part of a health service program for the employees. It was discovered that 8% of the employees needed corrective shoes, 15% needed major dental work and 3% needed both corrective shoes and major dental work. What is the probability that an employee selected at random will need either corrective shoes or major dental work?
Answer(s): A
8% + 15% - 3% = 20%
Eternal Life Insurance has a policy that will pay $50,000 per year starting 20 years from now, to you and all your progeny. If the appropriate discount rate is 10% per year and you have to pay premiums every year for the next 15 years starting at the end of this year, what's the annual premium payment that you and your heirs must make for this to be a fair deal?
You are entitled to a perpetuity which start paying 20 years from now. Therefore, at the end of year 19, you will have an asset worth $50,000/0.1 = $500,000. The present value of this equals $500,000/1.1^19 = $81,754.Your premium payments are a 15-year annuity. If the annual premium is P, then this annuity has a present value of P/0.1*[1 - 1/1.1^15] = 7.606P. This must equal the value of the perpetuity for this to be a fair deal. This gives P = $81,754/7.606 = $10,749.
Delroy McWilliams, a quantitative analyst with Churn Brothers Brokerage, is examining a data sample and has amassed the following information:Standard deviation of the sample: 70Number of observations: 600Sample mean: 812Assume that Mr. McWilliams formulates a null hypothesis that states that the value of the population mean is equal to 800. 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.
The standard error and test statistic for this example is 2.858 and 4.199, respectively. Therefore, none of these answers is correct.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 = [70 / 24.495] = 2.858}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 = [812 - 800] / 2.858 = 4.199}
Which of the following is/are true?
The lowest significance level at which the null hypothesis can be rejected is called the p-value of the test. Thus, if the p-value is less than the significance level, the null hypothesis can be rejected at that significance level; otherwise, you must fail to reject the null. The significance level in hypothesis testing refers to the probability that we will reject the null when it is true. Hence, if we always reject the null, the probability of rejecting it when it is true equals 1. A Type II error occurs when we fail to reject the null when in fact it is false. Therefore, if we always accept the null, we will never reject it even when it is false. So the probability of Type II error will equal 1.
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