STT 231 EXAM 2 QUESTIONS AND ANSWERS
What two conditions must be met in order for the CLT to apply for proportional testing? -
Answers :1: sample must be independent and identically distributed; like random
assignment/sampling
2: sample must be sufficiently large
Normal density curve - Answers :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? - Answers :the first number is
the mean (mu), and the second is the SD (sigma)
What is standard error? How do you interpret the results? - Answers :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? - Answers :as n increases, SE decreases, inverse
relationship.
Normal model for a sampling distribution of x bar - Answers :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? -
Answers :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? - Answers :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? - Answers :two commands required:
1: qqnorm(data set$variable)
2: qqline(data set$variable)
What would a straight qq plot indicate? - Answers :the 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? - Answers :right-skewed data
What would a concave down qq plot indicate? - Answers :the data is skewed/tailed to
the left
, What does an s shaped qq plot represent? - Answers :a 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? - Answers :apply the success-failure condition
What is the null distribution? - Answers :the sampling distribution based off of the null
value?
P-value - Answers :assuming 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
What is the equation for a standard normal curve/distribution, and what do the axes
represent? - Answers :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? - Answers :the actual domain=infinite, but we are interested mostly in (mu
+/- 3sigma)
Difference between pnorm and qnorm commands - Answers :pnorm: 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? - Answers :pnorm(upper cutoff,
mean, SD)
Qnorm(upper percentile cutoff, mean, SD)
When do you use the lower.tail=false argument? - Answers :during p/qnorm commands,
when you are interested in the right side distribution
Normal model for sampling distribution of pi hat - Answers :still follows the rule of
standard normal curve (N(0,1)), but it uses N(pi, SE equation) because
What do high and low p values mean in a general sense? - Answers :a high p-value
:0.10 means that 10% of the time, you could expect to see your sample statistic occur
under the null model, lower values 0.05 means that only 5% of the time would the null
distribution support your sample statistic
What are the various cutoff values for a p value? - Answers :less than 0.001 (extremely
strong evidence against null)
0.001 to 0.01 (very strong evidence)
0.01 to 0.05 (strong evidence)
0.05 to 0.10 (some evidence)
More than 0.10 (little evidence against null hypothesis)
What two conditions must be met in order for the CLT to apply for proportional testing? -
Answers :1: sample must be independent and identically distributed; like random
assignment/sampling
2: sample must be sufficiently large
Normal density curve - Answers :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? - Answers :the first number is
the mean (mu), and the second is the SD (sigma)
What is standard error? How do you interpret the results? - Answers :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? - Answers :as n increases, SE decreases, inverse
relationship.
Normal model for a sampling distribution of x bar - Answers :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? -
Answers :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? - Answers :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? - Answers :two commands required:
1: qqnorm(data set$variable)
2: qqline(data set$variable)
What would a straight qq plot indicate? - Answers :the 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? - Answers :right-skewed data
What would a concave down qq plot indicate? - Answers :the data is skewed/tailed to
the left
, What does an s shaped qq plot represent? - Answers :a 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? - Answers :apply the success-failure condition
What is the null distribution? - Answers :the sampling distribution based off of the null
value?
P-value - Answers :assuming 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
What is the equation for a standard normal curve/distribution, and what do the axes
represent? - Answers :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? - Answers :the actual domain=infinite, but we are interested mostly in (mu
+/- 3sigma)
Difference between pnorm and qnorm commands - Answers :pnorm: 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? - Answers :pnorm(upper cutoff,
mean, SD)
Qnorm(upper percentile cutoff, mean, SD)
When do you use the lower.tail=false argument? - Answers :during p/qnorm commands,
when you are interested in the right side distribution
Normal model for sampling distribution of pi hat - Answers :still follows the rule of
standard normal curve (N(0,1)), but it uses N(pi, SE equation) because
What do high and low p values mean in a general sense? - Answers :a high p-value
:0.10 means that 10% of the time, you could expect to see your sample statistic occur
under the null model, lower values 0.05 means that only 5% of the time would the null
distribution support your sample statistic
What are the various cutoff values for a p value? - Answers :less than 0.001 (extremely
strong evidence against null)
0.001 to 0.01 (very strong evidence)
0.01 to 0.05 (strong evidence)
0.05 to 0.10 (some evidence)
More than 0.10 (little evidence against null hypothesis)
