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: 2.90
Number of observations: 68 -
Degrees of freedom: 2 -
Sample mean: 114 -
Assume 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.
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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.