STT 231: EXAM 2 CORRECT 100%
what two conditions must be met in order for the CLT to apply for proportional testing? -
ANSWER1: sample must be independent and identically distributed; like random
assignment/sampling
2: sample must be sufficiently large
normal density curve - ANSWERsymmetric 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? - ANSWERthe 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? - ANSWERN(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? - ANSWERthe actual domain=infinite, but we are interested mostly in (mu
+/- 3sigma)
difference between pnorm and qnorm commands - ANSWERpnorm: gives
proportion/percent of data within the given range
qnorm: gives the cutoff range for the percentile of data inputted
what are the required arguments for pnorm? qnorm? - ANSWERpnorm(upper cutoff,
mean, SD)
qnorm(upper percentile cutoff, mean, SD)
when do you use the lower.tail=false argument? - ANSWERduring p/qnorm commands,
when you are interested in the right side distribution
normal model for sampling distribution of pi hat - ANSWERstill 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? - ANSWERit 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? - ANSWERas n increases, SE decreases, inverse
relationship.
normal model for a sampling distribution of x bar - ANSWERstill 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? -
ANSWERx 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? - ANSWERset 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? - ANSWERtwo commands required:
1: qqnorm(data set$variable)
2: qqline(data set$variable)
what would a straight qq plot indicate? - ANSWERthe sample data can be represented
by a normal distribution model (unimodal, no skew, centered at the mean)
what would a concave up qq plot indicate? - ANSWERright-skewed data
what would a concave down qq plot indicate? - ANSWERthe data is skewed/tailed to
the left
what does an s shaped qq plot represent? - ANSWERa plot that looks normally
distributed but the tails are either too fat/too thin (granularity differences) with few
outliers
how to predict whether your sample size is large enough to assume a normal
distribution? - ANSWERapply the success-failure condition
what is the null distribution? - ANSWERthe sampling distribution based off of the null
value?
p-value - ANSWERassuming the null hypothesis is true, the probability that you will
observe data as favorable or more favorable for the alternative hypothesis as the
current observed data
when is Cohen's H used? - ANSWERwhen you want to gauge how wrong/right the null
model is for a single-proportion test
what is the relationship between p value and effect size? - ANSWERas the effect size
becomes more extreme either positively or negatively, the p value decreases, because
the null model becomes more wrong
which statistics consider n, and which do not? - ANSWERsample size considered for p
value and test statistiscs, but not for effect size
what two conditions must be met in order for the CLT to apply for proportional testing? -
ANSWER1: sample must be independent and identically distributed; like random
assignment/sampling
2: sample must be sufficiently large
normal density curve - ANSWERsymmetric 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? - ANSWERthe 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? - ANSWERN(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? - ANSWERthe actual domain=infinite, but we are interested mostly in (mu
+/- 3sigma)
difference between pnorm and qnorm commands - ANSWERpnorm: gives
proportion/percent of data within the given range
qnorm: gives the cutoff range for the percentile of data inputted
what are the required arguments for pnorm? qnorm? - ANSWERpnorm(upper cutoff,
mean, SD)
qnorm(upper percentile cutoff, mean, SD)
when do you use the lower.tail=false argument? - ANSWERduring p/qnorm commands,
when you are interested in the right side distribution
normal model for sampling distribution of pi hat - ANSWERstill 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? - ANSWERit 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? - ANSWERas n increases, SE decreases, inverse
relationship.
normal model for a sampling distribution of x bar - ANSWERstill 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? -
ANSWERx 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? - ANSWERset 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? - ANSWERtwo commands required:
1: qqnorm(data set$variable)
2: qqline(data set$variable)
what would a straight qq plot indicate? - ANSWERthe sample data can be represented
by a normal distribution model (unimodal, no skew, centered at the mean)
what would a concave up qq plot indicate? - ANSWERright-skewed data
what would a concave down qq plot indicate? - ANSWERthe data is skewed/tailed to
the left
what does an s shaped qq plot represent? - ANSWERa plot that looks normally
distributed but the tails are either too fat/too thin (granularity differences) with few
outliers
how to predict whether your sample size is large enough to assume a normal
distribution? - ANSWERapply the success-failure condition
what is the null distribution? - ANSWERthe sampling distribution based off of the null
value?
p-value - ANSWERassuming the null hypothesis is true, the probability that you will
observe data as favorable or more favorable for the alternative hypothesis as the
current observed data
when is Cohen's H used? - ANSWERwhen you want to gauge how wrong/right the null
model is for a single-proportion test
what is the relationship between p value and effect size? - ANSWERas the effect size
becomes more extreme either positively or negatively, the p value decreases, because
the null model becomes more wrong
which statistics consider n, and which do not? - ANSWERsample size considered for p
value and test statistiscs, but not for effect size
