Ug statistics help

FINAL EXAM PREP FOR
UNDERGRADUATE
STATISTICS
© BN Heard
Not to be posted on any
websites, etc.
Intended to be downloaded
by students for their own
personal use

PREPARING FOR YOUR STATS
FINAL
First of all, know your basic terms and definitions.
This is just an overall picture of the types of questions generally found on
undergraduate statistics final exams.
There is no way to guess, I just try to hit a few.
In some cases, I give only one example, but be prepared for other types of
questions.
For example, I may give an example of a Poisson problem, but you should be
ready to answer a Binomial or Geometric distribution question if your course
covered those.
Also, with confidence intervals there are different types of situations.
Hopefully, what I have put together will help you remember what you learned in
your class and do better on your Final Exam.
I reference Minitab in most of the problem examples because most of my classes
use Minitab, however, I give the answers so that you can check your answers
using the technology of your choice.

FINAL
Levels of Measurement
The following are from records from a trainer of a football team.
Identify which of the levels of measurement each are (Either Nominal,
Ordinal, Interval or Ratio).
a) Number of visits to the whirlpool since the season started
b) General feeling after practice chosen from a scale of (Too Tired,
Normally Tired, Still Ready to Go)
c) Player's pre-practice body temperature.
d) Player's state of residence for insurance purposes.

FINAL
Answers to previous question
a) Interval, because 0 is the lowest number of visits you could have
b) Ordinal, because they can only be logically ranked
c) Body Temperature is actually Ratio because temperature can go
below zero (although we know that we could not survive)
d) Nominal, a state is just a label like a color

FINAL
Types of Sampling
What type of sampling? Stratified, Cluster, Convenience, Systematic, or
Simple Random.
a) A university asks every 10th student in line what they are majoring in.
b) 4 girls from each of 30 Girl Scout Troops are surveyed
c) One high school choir out of the 12 choirs in the district is randomly
chosen and all choir members are surveyed
d) The 17 members of the first grade class have all their names put in a hat
and one is drawn out to see who gets to sit next to the teacher
e) I ask everyone sitting at my lunch table who will win the Super Bowl

FINAL
What type of sampling? Stratified, Cluster, Convenience, Systematic,
or Simple Random.
a) Systematic
b) Stratified
c) Cluster
d) Simple Random
e) Convenience

FINAL
Descriptive Statistics
Find the range, mean, variance and standard deviation for the
following set of sample data.
12 13 15 11 19 9 21 19 14
Give the
Range
Mean (xbar)
Variance (s^2)
Standard Deviation (s)

FINAL
Answer to previous question
On this one, I simply used Minitab, some students use the formulas, Excel or other
software.
In Minitab, I input the data in Column C1, Labeling it "Data" (name doesn't matter)
Then I went to the Stat tab, chose Basic Statistics, Chose Descriptive Statistics
I put my cursor under in the Variables Box, then Double Clicked on the Data on the left I
wanted to analyze
I clicked the Statistics button and unchecked the things I didn't need and Made Sure
Range, Mean, Variance and Standard Deviation were checked.
I clicked Ok (for both windows) and got the following results in the Session Window
Descriptive Statistics: Data
Variable Mean StDev Variance Range
Data 14.78 4.09 16.69 12.00

FINAL
Understanding the difference between populations and samples
In a poll, 1300 American first graders were asked whether they liked
the smell of crayons or did not like the smell of crayons. Among the
respondents, 79% said they liked the smell of crayons. Identify the
population and the sample.

FINAL
Answer to the previous question
The population would be all American first graders.
The sample would be the 1300 who were asked the question
Also remember, populations give us parameters, samples give us
statistics.

FINAL
Understanding the difference between Qualitative and Quantitative
data
Determine whether the following variables are quantitative or
qualitative.
a) Color of a car
b) Pressure in the car’s tires
c) Your zip code
d) Number of whole potato chips in a bag

FINAL
a) Color of a car - Qualitative
b) Pressure in the car’s tires - Quantitative
c) Your zip code - Qualitative
d) Number of whole potato chips in a bag - Quantitative

FINAL
Problems involving Pivot Tables/Contingency Tables
Consider the following data from an ice cream truck operator,
specifically the information of the area of town of the customer and
the number of Choco Tacos ordered when the truck stopped.
(See Pivot Table on chart that follows)
If you choose a customer at random, then find the probability that the
customer is
a. from the South Side.
b. from the South Side and ordered 2 or more Choco Tacos.
c. East Side, given that the customer ordered only 1 Choco Taco.

FINAL

FINAL
a. from the South Side. 25/131 or 0.1908
b. from the South Side and ordered 2 or more Choco Tacos. Go within the table
because this is an “AND” 3/131 or 0.0229
c. East Side, given that the customer ordered only 1 Choco Taco. These are tricky,
any time you have a “given that” your denominator changes to only those you are
dealing with or the “given that” total.. So your answer would be 7/23 or 0.3043
Please note that if the question was worded “Ordered 1 Choco Taco, given that the
customer was from the East Side, the answer would be 7/57 or the decimal form

FINAL
Normal Distribution Problems
The mean amount of money spent on groceries by a family of four in
a given week is found to be $327 with a standard deviation of
$84.25. The distribution is known to be normally distributed.
a) Based on this information, find the probability the family would
spend less than $300
b) Based on this information, find the probability the family would
spend between than $275 and $390
c) Based on this information, find the probability the family would
spend more than $400

FINAL
Answers to previous question (I use Minitab, but you can use Excel or
Standard Normal tables/z scores etc.)
Using Minitab.
Go to Graph >> Probability Distribution Plot
Click View Probability (last one on the right)
Click OK
Make sure the distribution is set to “Normal”
Input 327 for the mean and 84.25 for the standard deviation
(Continued Next Page)

FINAL
Continued
Click the Shaded Area tab
a) For “less than $300”, Click radial button next to x-values, Click the Left Tail
icon because we want to know the probability that it is less than a value, input
300 for the x value, Click Ok
We see our answer is 0.3743 on the graph.
b) For “between than $275 and $390”, Click radial button next to x-values, Click
the Middle icon because we want to know the probability that it is between two
values, input 275 for x1 and 390 for x2, Click Ok
c) For “more than $400”, Click radial button next to x-values, Click the Right Tail
icon because we want to know the probability that it is greater than a value,
Input 400 for the x value Click Ok

FINAL
Other Normal Distribution type problems (concerning z scores,
Standard Normal Distribution, etc.)
For the standard normal distribution, find the probability of z being
between -1.26 and 1.15. You might even be given a graph with
coloring shown between these two z values on the bottom of the
graph.

FINAL
As I have noted in lectures, these questions pop up from time to time because of the use of tables in
statistics, in particular the standard normal distribution, z scores, etc.
I use Minitab, but you can easily do these using tables.
This is easy to solve with Minitab.
Go to Graph >> Probability Distribution Plot
Click View Probability (last one on the right)
Click OK
Make sure the distribution is set to “Normal”
Input 0 for the mean and 1 for the standard deviation (because we are dealing with the Standard
Normal and that is where z scores come from)
Click the Shaded Area tab (Next Chart)

FINAL
Answer Continued
After clicking the Shaded Area tab
Click radial button next to x-values (we ARE NOT putting in probabilities or
percentages etc.).
Click the Middle icon because we want to know the probability that it is
between two values
Input -1.26 for x1 and 1.15 for x2
Click OK
We get the attached graph (next chart) which shows us the probability is
0.7711 or 0.771 rounded to three decimal places.

FINAL
Continued

FINAL
Poisson Distribution Problems
Assume the Poisson Distribution applies. Use the given mean to find
the indicated probability.
Find P(4) when mu = 3.

FINAL
I used Minitab, but you can use Excel, tables, etc.
In Minitab, go the Calc Tab then Probability Distributions, Choose
Poisson
When the window comes up, click button next to "Probability"
Input Mean of 3
Click button next to "Input Constant" Enter 4 and hit ok
In the session window you see the answer is 0.168031 or 0.1680
rounded to four decimals or 0.168 rounded to three decimals

FINAL
Confidence Intervals
A random sample of 57 kitchen mixers have a mean price of $109
and standard deviation of $19.20. Find the 90% confidence interval
for the population mean.

FINAL
Answer to the previous question (You can use Minitab, formulas, other
technology, etc.)
I used Minitab
Go to Stat >> Basic Statistics >> 1 Sample Z (because you had more than 30
samples)
Input Sample Size of 57, Mean of 109 and Standard Deviation of 19.20.
Click Options and input 90 for your Confidence Level.
Click your OK buttons.
In the session window, you see that your 90% Confidence Interval is
($104.82, $113.18)
Note, if you would have had say 15 samples (less than 30), you would have
used a 1 Sample t in Minitab.

FINAL
Confidence Intervals (proportions)
In a survey of 9000 dog owners, 5400 say they walk their dogs at
least once per week. Construct a 95% confidence interval of the
population proportion of dog owners who walk their dogs at least
once per week.

FINAL
I used Minitab
In Minitab, Go to Stat >> Basic Statistics >> 1 Proportion
Click radial button next to summarized data
Input number of events 5400
Input number of trials 9000
Click Options button, set confidence level to 95%
Click Ok on both windows
In the session window, you see your answer is (0.5898, 0.6101) rounded to
four decimal places

FINAL
Sample Size Questions (Here is just one example)
People were surveyed on how many trips they made to the bank the
previous year. How many are needed to estimate the number of trips
they made the previous year to within one trip with 95% confidence?
Initial survey results indicate the population standard deviation sigma
is equal to 21.4 trips.

FINAL
The formula is
N = (zC s/E)^2
We find zC using Minitab or a table (most common ones in table to right).
s was given to be 21.4
E is 1 because it noted “within 1 trip”
N = (1.96 x 21.4/1)^2
N = (41.944)^2
N = 1759.2991 (BUT WE ALWAYS ROUND SAMPLE SIZES UP)
SO THE ANSWER IS WE NEED 1760

FINAL
Correlation/Regression Type Questions
Find the equation of the regression line of the given data. It gives
study hours (x) vs grade on final exam (y). Also give the correlation
coefficient “r.” In addition, predict scores for someone who studies
100 hours, 150 hours and 300 hours. Data Below.
"Study Hrs,
x"
"Grade,
y"
160 98
170 95
130 82
120 76
80 65
190 99

FINAL
Answer to previous question (I used Minitab, you can use the technology of
your choice)
This is a fun problem because being able to do regression is very valuable.
Get your data into Minitab. It copies and pastes nicely as always using the
little icon in the corner (above right of data, I always choose Make tab
delimited copy because it works well for me)
On this one, you simply go to Stat >> Regression >> Fitted Line Plot
You put your cursor in the box next to Response, then double click on your
“y” variable to the left. In our case this is the Grade. Now put your cursor in
the box next to Predictor and then double click on your “x” variable to the
left. In our case, this is the Study hours.
After clicking OK, you get a nice graph that you can use to compare to the
given choices if you are asked to do so.
(Continued on next chart)

FINAL
Answer continued
It also gives you the regression equation. On this one we got y = 38 + 0.3376x (Be careful to round to
the correct number of decimal places) For example if they said to round to three, this would be y =
38.000 + 0.338x . They give you the r^2 value in percentage form (94.5%). To get r you could take the
square root of the decimal form, or square root of 0.945 which is 0.972 rounded to three decimal
places.
To answer the other questions, you just “plug and chug” being careful to see if the given value is within
the range of data you were given.
So if we want to predict scores for someone who studies 100 hours, 150 hours and 300 hours.
For 100 hours we have y = 38.000 + 0.338(100) = 38 + 33.8 = 71.8 or 72 rounded to the nearest
whole number
For 150 hours we have y = 38.000 + 0.338(150) = 38 + 50.7 = 88.7 or 89 rounded to the nearest
whole number
For 300 hours, we would say that this would not be very meaningful because our study hours ranged
from 80 to 190. 300 is well outside of that range.
I'm attaching the Minitab graph result I got on the next page....

FINAL
Probability Type Questions
A cupcake company receives shipments of plastic decorations from
three different suppliers in quantities of 100, 200 and 500. Three
times a plastic decoration is selected at random, each time without
replacement. Find the probability that a) all three products came from
the 2nd supplier (assume suppliers are in order), b) none of the three
products came from the second supplier.

FINAL
a) (200/800)(199/799)(198/798) = 0.015 (rounded to three decimal
places)
b) (600/800)(599/799)(598/798) = 0.421 (rounded to three decimal
places)
Remember your total is going down….

FINAL
Hypothesis Testing (Basics)
Write the null and alternative hypothesis and identify the claim.
A recent survey showed the percentage of dogs that bite is equal to
45%.
Ho p = 0.45
Ha p ≠ 0.45
So the claim is the null in this case. However you have to remember
that the claim can be either the null or the alternative.

FINAL
More on the Basics of Hypothesis Testing
A recent survey of cab drivers showed more than 45% work more than 5 days a week
Ho p ≤ 0.45
Ha p > 0.45
The claim would be the alternative in this case.
Or
A recent survey of nurses showed at least 45% work more than 5 days a week
Ho p ≥ 0.45
Ha p < 0.45
The claim would be the null in this case because “at least” means 45% or 0.45 or more

FINAL
Hypothesis Testing Questions (There are many types, be familiar with
what your course has covered)
For a study on the number of bones that dogs consume in a given
week, you randomly select ten dog owners who give their dogs
bones. The results are listed at the right. At an a=0.05 is there
enough evidence to support the claim that dogs eat fewer than four
bones per week? Assume the population is normally distributed.
Note I use a for alpha and m for mu.
4.4
3.2
3.2
3.7
2.3
4.7
3.8
4.8
4.6
2.2

FINAL
Answer to previous question (I USED Minitab)
Input data into Minitab, use copy and paste function as I’ve shown in lectures.
I labeled my column “Bones” (It doesn’t matter).
Go to Stat >> Basic Statistics >> 1 sample t (because we only had 10 sample data
points)
Put cursor under Samples in Columns, then double click on Bones on the left or
whatever you called it…
Check box for “Perform Hypothesis Test”
Input 4 for Hypothesized Mean
Click Options button
Input 95 for confidence level (because our a is 0.05, the confidence is 1 – 0.05 or
0.95 or 95%
Make sure you choose “Less than” as your alternative because our alternative
hypothesis is m < 4
Click your ok buttons… (Next Chart)

FINAL
Answer continued
In the session window you will see
Variable N Mean StDev SE Mean Bound T P
Bones 10 3.690 0.956 0.302 4.244 -1.03 0.166
What does this mean?
Well, our p value of 0.166 is greater than our a of 0.05 which means we Fail to reject our null
hypothesis.
Remember the null hypothesis was that m >= 4 (the null always contains equality, in this instance, the
null was that the mean was greater than or equal to 4)
This means we do not accept the claim which was the alternative hypothesis that m < 4
So we would say, “There is not sufficient evidence to support the claim that dogs eat less than four
bones per week.”
Again above I used a for alpha and m for mu.

FINALI do this as a service to my statistics students and those who attend my online
lectures.
These charts are not to be posted by other instructors, schools, etc. without my
permission.
Want to thank me?
Never speak ill of statistics – Never say “Statistics Lie” – Because when done properly,
Statistical Analysis does not lie… Selective data, partial results and people might be
untruthful or skew results…
Other Ways to thank me…
Encourage children to do well in math and stress the importance…
Come see me at www.CranksMyTractor.com where I write about the good people,
places and things I find in life.
Like my CMT page on Facebook at www.facebook.com/cranksmytractor
Catch me on stage telling stories about the good things in life…

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