Formulae and Rules

Question 1

when is the data right skewed

Answer 1

when mean > median

Question 2

when is the data left skewed

Answer 2

when mean < median

Question 3

for a discrete random variable where X has a probability > 0.5, how do you compute P(X<=k)
hint: use Y

Answer 3

Let Y=n-k have a probability of 1-p
now P(X<=k)=P(Y>=n-k)=1-P(Y<=(n-k)-1)

Question 4

in terms of probability, when is a discrete random variable right skewed

Answer 4

if p<0.5

Question 5

in terms of probability, when is a discrete random variable left skewed

Answer 5

if p>0.5

Question 6

for a continuous random variable with a pdf why are P(x<=a) and P(x<a) the same

Answer 6

because P(X<=a) = P(X=a)+P(X<a) = 0+P(X<a)

Question 7

for a continuous random variable, how do you calculate P(a<=X<b)

Answer 7

P(X<=b) - P(X<=a)

Question 8

for a continuous random variable, how do you calculate P(X>=a)

Answer 8

1-P(X<=a)

Question 9

for Z with a standard normal distribution, how do you calculate P(Z>=-z)

Answer 9

P(Z<=z)

Question 10

for Z with a standard normal distribution, how do you calculate P(Z<=-z)

Answer 10

P(Z>=z)

Question 11

for Z with a standard normal distribution, how do you calculate P(-a<Z<a)

Answer 11

1-2P(Z>=a)

Question 12

what is (Ea1X1+…+anXn)

Answer 12

a1E(X1)+…+anE(Xn)

Question 13

if X1,…,Xn are independent random variables what is Var(a1X1+or-…anXn)

Answer 13

a1^2Var(X1)+…+an^2Var(Xn)

Question 14

what is the expectation of the random sample mean xbar=1/n(x1+…+xn)

Answer 14

the same as the expectation of X

Question 15

what is the variance of the random sample mean xbar=1/n(x1+…+xn)

Answer 15

the sample variance/sample size

Question 16

what is the standard deviation of the random sample mean xbar=1/n(x1+…+xn)

Answer 16

the standard deviation of X/sqrt(sample size)

Question 17

if X is normally distributed X~N(mu,sigma^2), how is the random sample mean distributed

Answer 17

Xbar~N(mu, sigma^2/n)

Question 18

for a one sample hypothesis test what is the rejection criteria for H0 when H1 is μ>μ0

Answer 18

test statistic > critical value

Question 19

for a one sample hypothesis test what is the rejection criteria for H0 when H1 is μ<μ0

Answer 19

test statistic < - critical value

Question 20

for a one sample hypothesis test what is the rejection criteria for H0 when H1 is μ doesn’t equal μ0

Answer 20

the absolute value of the test statistic is greater than the critical value

Question 21

what are the rejection criteria for one sample tests in terms of p value

Answer 21

p<significance level

Question 22

for a one sample hypothesis test what is the p value when H1 is μ>μ0

Answer 22

P(Z>=CalcZ)

Question 23

for a one sample hypothesis test what is the p value when H1 is μ<μ0

Answer 23

P(Z<=CalcZ)

Question 24

for a one sample hypothesis test what is the p value when H1 is μ doesn’t equal μ0

Answer 24

2P(Z>|CalcZ|)

Question 25

what is the criteria to pool variances

Answer 25

when at least one of the sample sizes is small and the two samples are normally distributed then 1/2 < s1^2/s2^2 < 2

Question 26

for a two sample test, what is the rejection criteria for H0 if μ1 > μ2

Answer 26

the test statistic > critical value

Question 27

for a two sample test, what is the rejection criteria for H0 if μ1 doesn’t equal μ2

Answer 27

the absolute value of the test statistic is > the critical value