STT 231: EXAM 2 QUESTIONS AND
ANSWERS 2026 VERIFIED.
What two conditions must be met in order for the CLT to apply for proportional testing? -
ANS 1: sample must be independent and identically distributed; like random
assignment/sampling
2: sample must be sufficiently large
normal density curve - ANS symmetric about the mean μ; has standard deviation σ; total area
under the curve = 1.0; values of the random variable X on x-axis; probabilities are represented
by areas under the curve;
what do the numbers in the N(0,1) equation represent? - ANS the first number is the mean
(mu), and the second is the SD (sigma)
what is the equation for a standard normal curve/distribution, and what do the axes represent?
- ANS N(0,1) the x axis represents z-scores, and the y is the probability
what is the domain for a standard normal curve? which particular interval are we interested in?
- ANS the actual domain=infinite, but we are interested mostly in (mu +/- 3sigma)
difference between pnorm and qnorm commands - ANS pnorm: gives proportion/percent of
data within the given range
qnorm: gives the cutoff range for the percentile of data inputted
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, what are the required arguments for pnorm? qnorm? - ANS pnorm(upper cutoff, mean, SD)
qnorm(upper percentile cutoff, mean, SD)
when do you use the lower.tail=false argument? - ANS during p/qnorm commands, when you
are interested in the right side distribution
normal model for sampling distribution of pi hat - ANS still follows the rule of standard
normal curve (N(0,1)), but it uses N(pi, SE equation) because
what is standard error? how do you interpret the results? - ANS it measures how close the
current sample data reflects the overall population predicted data, a high standard error value
represents that your sample is not very reflective of the population and is very spread out, vice
versa for low
how do SE and sample size n relate? - ANS as n increases, SE decreases, inverse relationship.
normal model for a sampling distribution of x bar - ANS still N(0,1) template, but the mean is
represented by mu, and the SD is sigma/square root of n
when should you use normal model sampling distribution of x bar and when for pi hat? -
ANS x bar if you are given mu in the problem, pi hat if you are given pi in the problem
if you are given a problem that gives the sample mean and asks for the proportion greater than
or equal to a z score, what would you do? - ANS set up the equation with the pnorm
command using the standard normal model, with pnorm(the value,0,1)
how do you create a qqplot in R? - ANS two commands required:
1: qqnorm(data set$variable)
2: qqline(data set$variable)
@COPYRIGHT ALL RIGHTS RESERVED PAGE 2 OF 7
ANSWERS 2026 VERIFIED.
What two conditions must be met in order for the CLT to apply for proportional testing? -
ANS 1: sample must be independent and identically distributed; like random
assignment/sampling
2: sample must be sufficiently large
normal density curve - ANS symmetric about the mean μ; has standard deviation σ; total area
under the curve = 1.0; values of the random variable X on x-axis; probabilities are represented
by areas under the curve;
what do the numbers in the N(0,1) equation represent? - ANS the first number is the mean
(mu), and the second is the SD (sigma)
what is the equation for a standard normal curve/distribution, and what do the axes represent?
- ANS N(0,1) the x axis represents z-scores, and the y is the probability
what is the domain for a standard normal curve? which particular interval are we interested in?
- ANS the actual domain=infinite, but we are interested mostly in (mu +/- 3sigma)
difference between pnorm and qnorm commands - ANS pnorm: gives proportion/percent of
data within the given range
qnorm: gives the cutoff range for the percentile of data inputted
@COPYRIGHT ALL RIGHTS RESERVED PAGE 1 OF 7
, what are the required arguments for pnorm? qnorm? - ANS pnorm(upper cutoff, mean, SD)
qnorm(upper percentile cutoff, mean, SD)
when do you use the lower.tail=false argument? - ANS during p/qnorm commands, when you
are interested in the right side distribution
normal model for sampling distribution of pi hat - ANS still follows the rule of standard
normal curve (N(0,1)), but it uses N(pi, SE equation) because
what is standard error? how do you interpret the results? - ANS it measures how close the
current sample data reflects the overall population predicted data, a high standard error value
represents that your sample is not very reflective of the population and is very spread out, vice
versa for low
how do SE and sample size n relate? - ANS as n increases, SE decreases, inverse relationship.
normal model for a sampling distribution of x bar - ANS still N(0,1) template, but the mean is
represented by mu, and the SD is sigma/square root of n
when should you use normal model sampling distribution of x bar and when for pi hat? -
ANS x bar if you are given mu in the problem, pi hat if you are given pi in the problem
if you are given a problem that gives the sample mean and asks for the proportion greater than
or equal to a z score, what would you do? - ANS set up the equation with the pnorm
command using the standard normal model, with pnorm(the value,0,1)
how do you create a qqplot in R? - ANS two commands required:
1: qqnorm(data set$variable)
2: qqline(data set$variable)
@COPYRIGHT ALL RIGHTS RESERVED PAGE 2 OF 7
