You are given n = 12, sum of the (X_i) = 2%, sum of the (X_i)^2 = 0.5%%. Find the sample standard deviation.
Answer(s): C
The sample standard deviation will be the positive square root of the sample variance. The sample variance will be determined using the computational formula [1/(n-1)] * {sum (as i goes from 1 to n) of (X_i)^2 - (1/n) * [sum (as i goes from 1 to n) of (X_i)]^2}. So we get 1/11 * (0.5 - 1/12*(2^2)) = 1.51%%. The positive square root of 1.51%% is 1.23%.
Sharleef Nettleton, a quantitative analyst with Churn Brothers Brokerage, is examining a data sample and has amassed the following information:Standard deviation of the sample: 2.90Number of observations: 68Degrees of freedom: 2Sample mean: 114Assume that Ms. Nettleton formulates a null hypothesis that states that the value of the population mean is 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.
Answer(s): D
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 = [2.90 / 8.2462] = 0.3517}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 = [114 - 0] / 0.3517 = 324.14}This is a very large test statistic and the null hypothesis will likely be rejected unless a very low level of confidence is employed.
If all the 10,000 data points in a regression lie exactly on a straight line, which of the following is/are true?
Answer(s): E
Since there is no error in the regression, the percentage of unexplained variance will be zero. The intercept and slope terms can be any real numbers and the correlation coefficient will be either + 1 or - 1.
Which is true of a leptokurtic distribution?
Answer(s): B
I and IV are true of leptokurtic distributions. This is also called having "excess kurtosis." II and III are characteristic of platykurtic distributions.
An experiment may have:
Answer(s): A
Experiments may have many outcomes.
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