### CFA Practice Question

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.
A. 0.3517; 324.14
B. 1.0199; 56.44
C. 0.3517; 84.34
Explanation: 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.

User Comment
Rguerra There is a large misconception here that got me totally on the wrong track. The question asks for the standard error of the estimate (abreviated SEE) which is a term used in regression analysis and where SEE = SQRT(SSR/(n-2)). I kept on trying to find the SSR but was not able to.

When I saw the answer, I realized the question was in fact looking for the "standard error of the sample" which is a completely different thing.
eddeb Assume null hypothesis is 0, when it's not given?
PedroEdmundo It's given, read again carefully!
steved333 Also, the sample is where the estimate comes from, so the sample standard error is the same as the estimate standard error. Either way you slice it, you can figure it out with std dev over sqrt n.
Mikehuynh Standard error = SD/n^0.5 = 2.9/68^0.5 = 0.3517
Friso eddeb: convention for null hypothesis is always: sample outcome represents population or normal distribution.
In this case null hypothesis: population mean=114, alternative: pop mean=0
alles Isn't the last phrase of the explanation wrong? The lower the level of confidence, the easier it is to reject the null.
adidas the lower the level of confidence, the wider the interval, and the easier to reject the null hypothesis.
gdelaorden Why are the "degrees of freedom" assigned a value of 2? Shouldn't it be n-1=67