Homework #1 – STAT 210 (29 points)

Look at Problem 1.1 found on pgs. 7 & 8 of the text. Make sure that you are able to match the answers in the back of the book. For those of you who are more mathematically inclined try Problem 1.13 on pg. 16.

Part I - Assigned Problems from the Text

  • Problem 1.2 on pg. 8 (2 pts.)
  • Problem 1.12 on pg. 16 (1 pt.)
  • Problem 1.14 on pg. 16 (2 pts.)

Part II - Simulation and an Introduction to How Hypotheses are Tested

In this problem you will be examining a similar problem to the Swain vs. Alabama example shown in class. As shown in class, we will use JMP to perform the simulations required rather than using a random digits table as described in section 1.2 of your text.

Description of the Problem:

The current treatment method for a certain form of leukemia amongst children has a 70% success rate. A new method has been developed that will hopefully improve the chance of successful treatment. Researchers hope to convince the medical community that this new method is better by performing a clinical trial. A sample of 50 patients is treated with the new method and 40 of these patients have a successful outcome.

Does this provide evidence that the new method is better?

a) Assuming the new method has the same success rate as the current method, generate 5 samples of size n = 50 from a population with .

To do this in JMP select New Data Table... from JMP Starterwindow and right click at the top of Column 1 and select Formula... from the drop-down menu. From the Functions section of the JMP calculator select Random > Random Binomial. In the random binomial expression change n to 50 and p (i.e. ) to .70. Finally click Apply followed by OK.

From the Rows pull-down menu select Add Rows... and add 5 rows to the spread sheet.

This will produce five simulated results for this experiment. You can easily divide these by 50 to obtain five realizations of the sample proportion/percentage. To do this in JMP double-click to the right of the first column to add a second column. In this column enter a formula that takes the results from Column 1 and divides by 50.

Report these five values for p. (2 pts.)

b) Use the five values obtained from part (a) to find the AV, MA, and RMS as shown in class and in your text. (6 pts.)

c) Assuming what is the? How does this compare to your RMS value from part (b)? (2 pts.)

d) Find an interval or range of values that should include roughly 95% of all values for obtained by sampling from a population where the success rate of the treatment method is and a sample size of is used.

How does this interval to help answer the main question of interest to the researchers?

(3 pts.)

e) Now add 9,995 rows to your simulation spreadsheet and construct a histogram of the results. To this in JMP select Analyze > Distribution and put the column containing the 10,000 values for in the Y, Columns box.

Note: you can use the Grabber to change the appearance of the histogram so it does not have any gaps.

Start with this End with this

How does the resulting histogram help answer the question of interest to the researchers? (3 pts.)

f) Using what you have seen in parts (a) – (e) do you think the researchers have proof beyond a reasonable doubt that the new treatment method has a higher success rate? Justify your answer. (4 pts.)

g) Use simulation and/or ideas presented in Chapter 1 to help make a ruling in the following Supreme Court case.

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The Supreme Court of the U.S. has made some important rulings that affect all subsequent trials in lower courts. In Casteneda vs. Partida (decided March 1977) the court noted that based on census figures 79% of the population in Hidalgo County had Spanish-sounding surnames. Of the 870 jurors selected to jury panels by the county, only 339 had Spanish-sounding surnames.

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Does this provide compelling evidence that jury panel selection was biased? Justify your answer. (4 pts.)

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