161SP03_LAB6

CJ 161 Statistical Analysis in Criminal Justice
Spring 2003
PAPER 4
DUE: 4/17/03

PURPOSE. The purpose of this lab is for you to do some hypothesis testing, using data and background from the Stinson-Marks 1993-1994 election fraud case. This is the first paper that asks you specifically to follow steps related to hypothesis testing, so you want to be sure to ask questions about any of those steps. The paper focuses largely on asking you to report on specific hypothesis-testing steps, but it also asks you to conclude with a short statement from a press release that reports in nontechnical terms on the results of your statistical test. The statistical test we are using is a z test of a proportion difference between a population and a large sample. You do not need a statistics program to do this lab - you can do this by hand or you can do it in a spreadsheet or you can use a pocket calculator you got as a gift for being a frequent flyer on FlyByNight Airlines. You can write up this lab as a series of steps - you do not need to make it a coherent paper like the previous ones.

FORMAT: No more than TWO pages typed, double spaced. SSN ONLY on each page; no names anywhere. References, if you have some, should be included WITHIN these two pages, not as an extra page. A page with calculations appended as a third page.

Step

Worth

What

1

10

NULL HYPOTHESIS. State your null hypothesis, framed with reference to the specific data. Do NOT just say: there will be no difference between the sample proportion and the population proportion (see note at end).

2

5

DESCRIBE in just a couple of sentences what your data represent

3

5

LEVEL OF MEASUREMENT. Describe the level of measurement of the variable in question

4

5

SIGNIFICANCE LEVEL. State your significance level

5

5

CRITICAL REGION. Is your test going to be a two-tailed test, or a one tailed test? (This is obvious because you already know that the proportion voting for Stinson on the absentee votes was much higher than the proportion voting for him on the machine vote. But you still need to state this explicitly because it tells you how big your critical z value is. You may want to state your Z critical explicitly

6

5

Z OBTAINED. State your z obtained, from your calculations. You will use Eq. 10.5 on p. 283 in B&P to get your z obtained.

7

5

STATE: do you reject or fail to reject your null hypothesis? (if Z obtained is further from 0 than Z critical, you do what?

8

50

SUMMARY STATEMENT FOR THE NEWSPAPER. You want a statement, at least four to six lines long, that translates the implications of your statistical test into NONTECHNICAL terms for a typical reader of the Daily News. This is where you interpret your test. NOTE - if you have an incorrect result but you interpret it properly, you can still get full credit for this section!

9

10

APPEND a page that has your calculations on it. Be sure it has clearly labeled (using B&P's terminology on p. 283) p [the population proportion voting for Stinson, which in this case will be the machine proportion] p-hat [the sample proportion voting for Stinson] and {sqrt(p*q)/n} [the standard deviation of the sampling distribution or the standard error of the proportion.] NOTE: you get credit for this section regardless of whether your calculations are correct or not! You MAY append the filled in spreadsheet for calculations if you want.

EXTRA CREDIT: go to http://www.psychstat.smsu.edu/pdf/pdfj.htm and calculate the exact "area" above this z score; this translates to the EXACT probability of getting an outcome this extreme or more extreme.

NOTE. We are making a simplifying assumption in setting up this test this way. We are assuming that in the November 1993 the absentee ballots are a representative, random sample of a larger population of eligible voters, whose behavior we know about through the results of the machine vote. An alternative approach is to presume that during this election, and during earlier senatorial elections in the Second District, the proportion voting Democratic by machine, and the proportion voting Democratic by absentee ballot, are always somewhat different. That's why Ashenfelter got the voting history data, as described in the newspaper articles.

Step	Worth	What
1	10	NULL HYPOTHESIS. State your null hypothesis, framed with reference to the specific data. Do NOT just say: there will be no difference between the sample proportion and the population proportion (see note at end).
2	5	DESCRIBE in just a couple of sentences what your data represent
3	5	LEVEL OF MEASUREMENT. Describe the level of measurement of the variable in question
4	5	SIGNIFICANCE LEVEL. State your significance level
5	5	CRITICAL REGION. Is your test going to be a two-tailed test, or a one tailed test? (This is obvious because you already know that the proportion voting for Stinson on the absentee votes was much higher than the proportion voting for him on the machine vote. But you still need to state this explicitly because it tells you how big your critical z value is. You may want to state your Z critical explicitly
6	5	Z OBTAINED. State your z obtained, from your calculations. You will use Eq. 10.5 on p. 283 in B&P to get your z obtained.
7	5	STATE: do you reject or fail to reject your null hypothesis? (if Z obtained is further from 0 than Z critical, you do what?
8	50	SUMMARY STATEMENT FOR THE NEWSPAPER. You want a statement, at least four to six lines long, that translates the implications of your statistical test into NONTECHNICAL terms for a typical reader of the Daily News. This is where you interpret your test. NOTE - if you have an incorrect result but you interpret it properly, you can still get full credit for this section!
9	10	APPEND a page that has your calculations on it. Be sure it has clearly labeled (using B&P's terminology on p. 283) p [the population proportion voting for Stinson, which in this case will be the machine proportion] p-hat [the sample proportion voting for Stinson] and {sqrt(p*q)/n} [the standard deviation of the sampling distribution or the standard error of the proportion.] NOTE: you get credit for this section regardless of whether your calculations are correct or not! You MAY append the filled in spreadsheet for calculations if you want.
		EXTRA CREDIT: go to http://www.psychstat.smsu.edu/pdf/pdfj.htm and calculate the exact "area" above this z score; this translates to the EXACT probability of getting an outcome this extreme or more extreme.
NOTE. We are making a simplifying assumption in setting up this test this way. We are assuming that in the November 1993 the absentee ballots are a representative, random sample of a larger population of eligible voters, whose behavior we know about through the results of the machine vote. An alternative approach is to presume that during this election, and during earlier senatorial elections in the Second District, the proportion voting Democratic by machine, and the proportion voting Democratic by absentee ballot, are always somewhat different. That's why Ashenfelter got the voting history data, as described in the newspaper articles.