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Summer 2007 Stats Exam 2: Analyzing Independence, Marital Issues, and Process Control - Pr, Exams of Data Analysis & Statistical Methods

University of Idaho (U of I)Data Analysis & Statistical Methods
Prof. Rick L. Edgeman

The second examination for statistics 251, held in summer 2007. The exam covers various topics, including testing independence, identifying important marital issues, and process control in manufacturing. Students are required to calculate test statistics, provide decision rules, and interpret results. The document also includes data sets for analysis.

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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Statistics 251 –Examination Two – Summer 2007
NAME: __________________________ STUDENT ID: _________________
I pledge on my honor that I have not given or received any unauthorized assistance on this
examination. ____________________________ ______________________________
Signature Date
Setting One (Questions 1 through 4: 25 Points): Below you should recognize a problem
from the first exam. In that exam you were asked to determine whether independence held for a
specific cell. Let’s revisit the problem now and – this time – let’s test to see whether “State in
which a crime is reported” and “whether or not the crime report is meth-related” are independent
or dependent. Do so at the α = .05 level of significance. The original description follows …..
ORIGINAL DESCRIPTION: Both Washington and Oregon have enacted stronger laws related
to meth-production, distribution, and use than has Idaho. This has led some meth-labs formerly in
Washington and Oregon to relocate to Idaho. Advocates of tougher meth laws believe that as a
result of this Idaho may have a higher proportion of meth-related crimes than do Washington and
Oregon. A random sample of 1,000 crime reports gave the following results.
STATE
CRIME REPORTS
Meth-Related Not Meth-Related Totals
Idaho 100 150 250
Washington 105 245 350
Oregon 120 280 400
Totals 325 675 1,000
1. Provide H0 and HA in sentences specific to the problem (6 points)
H0:
HA:
2. Provide the complete decision rule (6 points)
DR:
3. What is calculated value of the test statistic? χ2calc = __________ (7 points)
4. Provide a reasonable and context specific interpretation of results (6 points)
Statistics 251-Summer 2007 - Examination Two
4 pages total
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Statistics 251 –Examination Two – Summer 2007

NAME : __________________________ STUDENT ID : _________________

I pledge on my honor that I have not given or received any unauthorized assistance on this examination. ____________________________ ______________________________ Signature Date

Setting One (Questions 1 through 4: 25 Points): Below you should recognize a problem

from the first exam. In that exam you were asked to determine whether independence held for a specific cell. Let’s revisit the problem now and – this time – let’s test to see whether “State in which a crime is reported” and “whether or not the crime report is meth-related” are independent or dependent. Do so at the α = .05 level of significance. The original description follows ….. ORIGINAL DESCRIPTION : Both Washington and Oregon have enacted stronger laws related to meth-production, distribution, and use than has Idaho. This has led some meth-labs formerly in Washington and Oregon to relocate to Idaho. Advocates of tougher meth laws believe that as a result of this Idaho may have a higher proportion of meth-related crimes than do Washington and Oregon. A random sample of 1,000 crime reports gave the following results. STATE

CRIME REPORTS

Meth-Related Not Meth-Related Totals

Idaho 100 150 250 Washington 105 245 350 Oregon 120 280 400

Totals 325 675 1,

1. Provide H 0 and HA in sentences specific to the problem (6 points) H 0 : **HA:

  1. Provide the complete decision rule (6 points)** DR:

3. What is calculated value of the test statistic? χ

2 calc = __________ (7 points)

4. Provide a reasonable and context specific interpretation of results (6 points) Statistics 251-Summer 2007 - Examination Two

SETTING TWO: (Questions 5 through 8: 25 points) A recent survey gathered responses

from a sample of 500 married women and a second sample of 500 married men. Among the goals of the work were to identify issues regarded as most important in a marriage and to determine whether there were any gender differences. Given the data below, test the appropriate hypothesis at the α = .10 level of significance.

SINGLE MOST IMPORTANT ISSUE

GENDER

Faithfulness Shared Religious and Moral Perspectives Shared Views on Child Raising Shared Financial Vision & Priorities Equitable Division of Household

Duties TOTAL

Women 220 160 65 35 20 500

Men 180 140 85 65 30 500

TOTAL 400 300 150 100 50 1,

5. Provide H 0 and HA in sentence form with words specific to the issue (6 points). H 0 : **HA:

  1. Provide the complete decision rule (6 points).** DR:

7. What is the calculated value of the test statistic? χ

2 calc = __________ (7 points)

8. Provide a reasonable and context specific interpretation (6 points) Statistics 251-Summer 2007 - Examination Two

Setting Four: (Questions 15 through 20: 25 points): Refer back (as needed) to the

description of I^3 at the beginning of “Setting Three”. Suppose that I^3 has another process that

prints on poster material of a specific size (16” x 20”). I^3 is concerned with the number of defects

per poster and may elect to pursue an improvement strategy, depending on what is revealed by a control chart for the process. Every 100th^ poster produced is sampled. Recorded in the table below are the number of defects for the first 20 posters sampled (in order): Poster 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total Defect s 3 0 1 2 7 1 1 1 0 2 1 0 0 0 1 2 1 0 0 2 25

**15. What type of control chart should be used? _______________ (2 points)

  1. What is the value of the Center Line on the chart? CL = __________ (3 points):
  2. What is the value of the needed standard deviation (SD)? SD = __________ (4 points)
  3. What are the coordinates for the remaining six lines on the control chart? (6points)** U1SL = __________ L1SL = __________ U2SWL = __________ L2SWL = __________ **UCL = __________ LCL = __________
  4. ACCURATELY plot the defects data on the control chart below. Be sure to record the** coordinates for the seven lines to the right of each line (that is, CL, U1SL, etc.)(5 points) UCL ________________________________________________________________________________________ U2SWL ________________________________________________________________________________________ U1SL ________________________________________________________________________________________ CL ________________________________________________________________________________________ L1SL ________________________________________________________________________________________ L2SWL ________________________________________________________________________________________ LCL ________________________________________________________________________________________ Poster 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20. Apply the appropriate PATS. Discuss the results of each of these and whether the

process is in-control or out-of-control. Then discuss how I

3 might use this information to begin to improve the process. (5 points). Statistics 251-Summer 2007 - Examination Two