lecture 2 - statistical inference

Question 1

what happens to a distribution curve when the number of observations gets larger (approaches infinity) and the width of each sample gets smaller (approaches 0)

Answer 1

get a smooth curve of an underlying probability distribution

Question 2

true/false: for a normal distribution, the mean, median and mode are the same

Answer 2

true

Question 3

what is the AUC of a normal distribution?

Answer 3

AUC =1 with 50% below to mean and 50% above the mean

Question 4

the shape of a NORMAL CURVE can be defined by what two factors?

Answer 4

1. σ^2 (sigma) - population variance
2. μ (mu) - population mean

Question 5

for two normal distributions where the population variance, σ^2, ______ (equal/don’t equal) each other and the population mean, μ, _______ (equal/don’t equal) each other, the density function will have the SAME shape but will be at different locations on the x-axis

Answer 5

equal; don’t equal

Question 6

for two normal distributions where the population variance σ^2, ______ (equal/don’t equal) each other and the population mean, μ, _______ (equal/don’t equal) each other, the density function will have DIFFERENT shapes but will all be at the same location on the x-axis

Answer 6

don’t equal; equal

Question 7

this determines the location of the curve

Answer 7

mean/ μ

Question 8

this determines the distributions shape (peakedness and spread)

Answer 8

population variance/σ^2

Question 9

the _______ (smaller/larger) the variance, the more speed and less peak

Answer 9

larger

Question 10

the _______ (smaller/larger) the variance, the less spread and more peak

Answer 10

smaller

Question 11

following the normal distribution empirical rule, __% of observations fall within one standard deviation of the mean

Answer 11

68%

Question 12

following the normal distribution empirical rule, __% of observations fall within two standard deviations of the mean

Answer 12

95%

Question 13

following the normal distribution empirical rule, __% of observations fall within three standard deviations of the mean

Answer 13

99.7%

Question 14

we can use the properties of the normal distribution to define these types of values

Answer 14

typical and atypical

Question 15

this value is = to the mean (μ) ± one standard deviation (σ)
which is equal to 68.26% of our population

Answer 15

representative or typical values

Question 16

this value is outside of the mean (μ) ± 3 standard deviations (3σ) which includes 99.74% of our population

Answer 16

unrepresentative or atypical values

Question 17

this value is within the mean (μ) ± 2 standard deviations (2σ) which includes 95.44% of our population

Answer 17

somewhat representative values

Question 18

a standard normal distribution has a mean (μ) of ____ and a standard deviation (σ) of _____

Answer 18

0;1

Question 19

how can other normal distributions (don’t have mean of 0 or standard deviation of 1) be transformed into the standard normal deviation?

Answer 19

z-score

Question 20

what is the formula for z-score?

Answer 20

z = (x-μ)/σ