A sample of size 3,000 of apples has the total sum of weights equal to 1785 pounds, and total sum of squared weights equal to 3823470. The estimate of the standard error of sample mean is:
Select one: a. 0.004858 b. 0.005344 c. 0.004417
Estimator X for a population parameter has a sampling distribution with the least variance. Estimator Y approaches the true value of population parameter when the sample size becomes large. The expected value of estimator Z equals the true value of the population parameter. X, Y, and Z are:
Select one: a. unbiased, consistent, and efficient respectively. b. unbiased, efficient, and consistent respectively. c. efficient, consistent, and unbiased respectively.
There are 10,000 stocks in the market. You wish to estimate the mean Sharpe Ratio for these stocks, so you take a random sample of size 144. The average Sharpe Ratio for the sample is 0.4851. The standard deviation for the population is known to be 0.3082. The 95% confidence interval for the population mean Sharpe Ratio is:
Select one: a. 0.4348 0.5354 b. 0.4190 0.5512 c. 0.4429 0.5273
Which of the following is false?
Select one: a. The probabilities for different possible values of a random variable with a discrete uniform distribution are equal. b. A random variable with a binomial distribution can take one of two possible values. c. The probabilities for different possible values of a random variable with a continuous uniform distribution are equal.
This is just definitional. There really is not much to explain. An estimator is a rule (or formula) for calculating a parameter (which is a true but often unobservable characteristic of a population). For instance, the sample mean is an unbiased estimator of the population mean.
All estimators have properties, which may be used to pick and choose the best. Usually, one prefers unbiased, efficient, and consistent estimators. Colloquially, unbiasedness means that on average the estimator does not miss. Efficiency implies that it misses the least. And, consistency implies that is misses less as N grows.
The general structure of a confidence interval for the population mean is: point estimate +/- critical value * standard error. The right-hand product is also referred to as the margin of error. The point estimate is 0.4851. The critical value corresponding to a two-sided test at alpha=5% is 1.645 (you are not expected to know this on the exam). The standard error is the population standard deviation divided by the square root of the # of observations. This follows from the Central Limit Theorem, which clearly applies since the number of observations (144) exceeds the often used n=30 threshold.
Putting words into numbers, the 95% CI is: 0.4851 +/- 1.645 * 0.3082 / 12, or C.
A is true. C is too, except all the probabilities are equal to 0 in this case. B is false; it is trying to have you confuse the binomial distribution with a bernoulli trial. The former is the distribution of successes in a series of the latter, and hence it (the binomial) can take more than two possible values.
This looks like FRM Quant level haha, so don’t even fret if you don’t understand it in one go. It relies on an alternative definition of variance: E(x^2) - E(x)^2.
3823470 / 3000^2 - (1785/3000)^2 = 0.070805 (sample variance)
standard error of sample mean = sqrt(0.070805) / sqrt(3000) = 0.004858
Again, this is beyond the scope of Level 1 for sure.
Also, where did these questions come from? They don’t read like CFAI.
I wouldn’t provide more assistance to this guy this looks more like a homework assignment than CFA review for studying, also just pasted questions no write up as to what he tried where he got stuck, what he doesnt understand
I agree. It’s good practice, though.
Orang3eph, you know your stuff. Are you only a level 1 candidate? If so, you must have a strong background.
Thanks buddy. Yeah, I’m only a L1 (sat in June), but also a recent (June) college grad so some of the econometrics is still fresh. I’m studying for the November FRM exam too.