JMP Assignment 3
t-Tests
Analyze the data given in Problem 9.12 using JMP. Hand in
the JMP output and highlight your answers. Don't attempt to answer the questions asked in
9.12 but do answer the questions listed below.
Follow the following steps to do this problem:
Create a JMP dataset with 2 columns: one to identify the sample a data
point comes from (we'll just name it "sample") and one for the data
itself (we'll name it "data").
File -> New to open a new data table
Click once between the two boxes above the column labeled Column 1
to select that column. Click Cols -> Column Info to set
the properties for this column. Change the Column Name to "sample" and
change Data Type to Character. Click on OK to close the box.
Double click to the right of the "sample" column to
create a new column. Repeat the above procedure to change the name of the new column to
"data", but leave the Data Type as Numeric.
Rows -> Add Rows and add 31 rows.
Fill in the data. Enter the number 1 in the first 15 rows of the sample
sample and 2 in the last 16 rows of the sample column. Enter the data in the
second row, the Sample 1 data in the first 15 rows and the Sample 2 data is in the last 16
rows.
Analyze -> Fit Y by X Click
on "sample" and then ">> X >>" and
click on "data" and then ">> Y >>".
Click on OK. A new window with a plot of the data is displayed.
Click on the box to the right of Analysis. Click on the
Quantiles item. Repeat until the first three items are checked (Quantiles;
Means, Anova/t-Test; and Means, Std Dev, Std Err). Under Display
make sure only the first three items are checked there as well (Show Points, Quantile
Boxes, Means Diamonds).
Print and pass in the resulting output. Answer the
following questions:
Question 1. Quantiles are given in the first text box
labeled Quantiles. What is the median and IQR (given as a pair of numbers) for
each sample.
Question 2. The last text box is labeled Means and
Std Deviations gives means, sample standard deviations, sample standard errors of the
mean and sample sizes. Use this data to form a small-sample 95% confidence interval for
each population mean (the population sample 1 was drawn from and the population sample 2
was drawn from).
Question 3. The test statistic and p-value for the
two-tailed hypothesis are given in the box labeled t-Test. What are the
two-tailed null and alternative hypotheses here? What is your conclusion about these
hypotheses (would you reject or fail to reject the null and why).
Multinomial Tests
Do Problems 14.6 and 14.7(a) using JMP. Hand in the JMP
output and highlight your answers. Be sure to state whether you reject the null hypothesis
or not and why.
As an example of how to do this I'll describe how to use JMP to solve
Example 14.1 on page 689 of the book.
Create a JMP dataset with 2 columns, one for outcome (we'll just name it
"outcome") and one for the number of trials with that outcome (we'll
name it "freq").
File -> New to open a new data table.
Click once between the two boxes above the column labeled Column 1
to select that column. Click Cols -> Column Info to set
the properties for this column. Change the Column Name to "outcome" and
change Data Type to "Character".
Double click to the right of the "outcome" column to
create a new column. Use the above procedure to change the name of the column to "freq"
but leave the data type as "Numeric". After you're done click once on
the box on the top right of the column and select "Freq".
Rows -> Add Rows and add 4 rows.
Fill in the data, the numbers 1 through 4 in the "outcome"
column and 39, 99, 336 and 26 in the second column.
Analyze -> Distribution of Y
Click on "outcome" and then ">> Add >>"
and make sure "freq" is listed in the ">> Freq >>"
box.
On top of the resulting output click on the box to the right of "outcome"
and click on "Test Probabilities". Click on each of the symbols
(probably either question marks or dots) in the column labeled "Hypoth Prob" on
the new box and enter, from top to bottom: 0.07, 0.18, 0.65 and 0.10 and click on "Done".
The Pearson statistic should be the same as the Chi-squared value on the top of page 690.
Tests of Independence
(Death Penalty Example)
We will look at data resulting from 326 defendants in homicide indictments
in 20 Florida Counties between 1976-1977. The race of the defendant, the race of the
victim and whether or not the defendant received the death penalty are reported. The
dataset is named deathpen.jmp and is available here and on the Mathlab1 Server. You may want to look here for instructions on how to access the data from the Mac labs
and over the internet.
Do not write your answers on the JMP output, use separate pieces of paper.
However, print out and pass in all JMP output you used to answer your questions. Indicate
on the JMP output where you got your answers (for instance, write "Q1" near the
contingency table on the output from the above analysis).
First we'll look at the relationship between the defendant's race and
conviction.
Analyze -> Fit Y by X.
Click on "Defendant" and then click on ">> X >>"
to add defendant's race to the "X" list. Now click on "Death"
and then ">> Y >>" to add the outcome of the
death penalty to the "Y" list. Make sure "Frequency" is in
the ">> Freq >>" list and click "OK".
Question 1: What is the overall probability of receiving
the death penalty. (Hint: Click on the box to the left of "Crosstabs"
and select "Total %".
Question 2: What is the probability of receiving the
death penalty given that the defendant is black? (Hint: Click on the box to the left of "Crosstabs"
and select "Col %".)
Question 3: What is the probability of receiving the
death penalty given that the defendant is white?
Question 4: Use the Pearson test to investigate whether
the outcome of a death penalty case is dependant on the defendant's race. What exactly is
the hypothesis you are testing? What is the p-value? What is your conclusion?
Repeat the analysis described above to investigate the relationship
between the victim's race and receiving the death penalty.
Question 5: What is the probability of a defendant
receiving the death penalty given that the victim was black?
Question 6: What is the probability of a defendant
receiving the death penalty given that the victim was white?
Question 7: Use the Pearson test to investigate whether
the outcome of a death penalty case is dependant on the victim's race. What exactly is the
hypothesis you are testing? What is the p-value? What is your conclusion?
Question 8: What seems to influence the assignment of the
death penalty more, the race of the defendant or the race of the victim?
