# Quant Q Bank Question

A local high school team had 18 homes games and averaged 58 pts per game. Pts per games is normally distributed, what is the range for a confidence interval of 90%? a - 26-80 b - 24-78 c - 34-82 d - 62-74 Thanks

is it A?

no its C, any ideas?

got a standard deviation?

no, that’s what’s confusing to me

What does the solution say (not the answer, but how derived)?

this question cannot be solved as the standard deviation is not mentioned… the normal distribution is defined by mean and std deviation… so we cannot know the shape of the normal distribution curve… so the range can only be figured out wen we know the sd…

This question is actually fairly easy. Go back to your standard error formula. You can use the mean for the numerator just like in a sample population. use (n-1) for the demoninator, for conservativeness just because you don’t have the variance or std dev. So… 58 / sq root (18-1) = 58 / 4.123 = 14.067 C.I = points per game ± (90% confidence)(14.067) = 58 ± (1.65)(14.067) = 58 ± 23.211 range = 34.78 to 81.211. answer is C for the purposes of the exam, you can round your answers a little bit. The choices on the test will not be so close that some shortages in your decimal points will make a big deal hope that helps…mike

Isn’t the numerator in the Std Error formula – either sd (sample std dev) or the population std dev (sigma)? Then how are you able to use a Average (mu) in the numerator and then claim that the problem is rather easy? There is absolutely nothing provided to you to be able to calculate variance / std deviation, unless this is something completely new. std dev when I last checked was sqrt (variance) and variance = Sum over i of (Xi - XBar)^2 / (n - 1) are u claiming that Xi is all zero? If so, how did all zero Xis come to result in an average XBar of 58?

cpk123, its all in the section under “confidence interval estimate of a population parameter.” PP280-281 in the Schweser notes. There is very very little on this exam that will fit into a formula nice and clean. Most of the problems on the exam test your knowledge of the concepts…

Where do they tell you in those two pages that Std Devn is the mean / sqrt (n-1)? I am pretty sure there is a reasonable explanation somewhere – which states that this problem is missing either the sample or population Standard deviation.

Guys this is a very simple question and the solution lies in calculating mean of CIs given. For A) mean is 53 = (26+80)/2 and actual mean is 58 —> incorrect you can calculate rest of the means … only C has the correct mean that is 58, and C is the correct answer

Yep as Madanalyst says only C is centered on 58. (You can also use this CI to calc sd.)

ah crikey, that’s a sneaky one (for me at least)