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1.In the following description of data, identify the W’s(who, what, when, where, why, how), name the variables, classify each variable as categorical or quantitative, and for any quantitative variable, identify the units in which it was measured (or note that they were not provided):

The State Education Department requires local school districts to keep these records on all students: age, race or ethnicity, days absent, current grade level, standardized test scores in reading and mathematics, and any disabilities or special educational needs.

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Who: students

What: age, race or ethnicity, days absent, current grade level, standardized test scores in reading and mathematics, and any disabilities or special educational needs

Why: State Education Department Guidelines for local school districts

How: not specified

When: not specified

Where: local school district

Variable
Categorical/Quantitative
Units
Description
age
Quantitative
Not provided (years)
Student’s age in years
race
Categorical

Race or ethnicity of the student
absent
Quantitative
days
Number of days absent from school
CGL
Quantitative
Not provided (decimal/percent)
Student’s current grade level
mathscore
Quantitative
Not provided (percentile)
Student’s standardized test scores in mathematics
readscore
Quantitative
Not provided (percentile)
Student’s standardized test scores in reading
other
Categorical

Any disabilities or special educational needs of the student

2. In the following description of data, identify the W’s, name the variables, classify each variable as categorical or quantitative, and for any quantitative variable, identify the units in which it was measured (or note that they were not provided):

The Gallup Poll conducted a representative telephone survey of 1180 American voters during the first quarter of 2007. Among the reported results were the voter’s region (Northeast, South, etc.), age, party affiliation, and whether or not the person had voted in the 2006 midterm congressional election.

Who: American Voter

What: region, age, party affiliation, and whether or not voted in the 2006 midterm congressional election

Why: To know voter choice for representative

How: Telephone survey

When: The first quarter of 2007

Where: America

Variable
Categorical/Quantitative
Units
Description
region
Categorical

Voter’s region (Northeast, South, etc.)
age
Quantitative
Not provided (years)
Voter’s age in years
partyaff
Categorical

Voter’s party affiliation
V2006
Categorical

The person (voter) had voted in the 2006 midterm congressional election (yes, or no).

3. A study in California looked at the impact of pregnant women smoking on the birth weight of their children. The study involved over 1000 mothers.

Here is a table produced by the authors of the study.

Variable
Description
bwt
Infant birth weight in ounces
gestation
Length of pregnancy in days
parity
0= first born, 1 = other
age
mother’s age in years
height
mother’s height in inches
weight
Mother’s prepregnancy weight in pounds
smoke
Smoking status of mother: 0= not now, 1=yes now

(a) What do you think the cases/individuals are in this study?

The individuals in the study are pregnant women from California and the cases are the impact of pregnant women smoking on the birth weight of their children.

(b) Which of the variables are categorical? Explain your answer.

The variables parity and smoke are categorical.  The variety parity is categorical because it is coded attribute and here words rather than numbers describe values. Similarly, the smoke variable is categorical because it is coded attribute and here words rather than numbers describe values.

4. Listed below are six categorical variables. For each variable, indicate whether it is ordinal or nominal. In each case explain your answer.

Nominal data merely identify a category. Ordinal data codes connote a ranking of data values.

(a) Type of hospital (public, private not-for-profit, or private for-profit)

Nominal: Here type of hospital only identifies a category.

(b) A person’s usual level of activity (slight, moderate or a lot)

         Ordinal: Here person’s usual level of activity connotes a ranking.

(c) A person’s level of agreement with a statement about health insurance (strongly agree, somewhat agree, neutral, somewhat disagree, strongly disagree)

Ordinal: Here person’s level of agreement with a statement about health insurance connotes a ranking.

(d) Massachusetts County (Berkshire, Dukes, Essex, etc.)

Nominal: Here Massachusetts County only identifies a category.

(e) Severity of asthma in children (mild intermittent, mild persistent, moderate persistent, or severe persistent)

Ordinal: Here Severity of asthma in children connotes a ranking.

(f) Sources of back pain (muscles, ligaments, tendons, bones, joints, or disc)

Nominal: Here Sources of back pain only identifies a category.

5. A study by the U.S. Bureau of Alcohol, Tobacco and Firearms (BATF) (USA Today, 22 June 2000) surveyed 1530 investigations by the U.S. BATF into illegal gun trafficking from July 1996 through December 1998. The study reports the portion of cases that were the result of each of five gun trafficking violations:

46% Straw purchase (legal gun buyer acting on behalf of an illegal buyer.)
21% Unlicensed sellers
14% Gun shows and flea markets
14% Stolen from federally licensed dealers
10% Stolen from residences

a) State the W’s for this study to the extent the story gives them.

The study conducted by BATF is related to investigation into illegal gun trafficking from July 1996 through December 1998 and reports the portion of cases that are the result of each of five gun trafficking violations straw purchase, unlicensed sellers, gun shows and flea markets, stolen from federally licensed dealers, and stolen from residences.

Who: investigations

What: illegal gun trafficking cases from July 1996 through December 1998

Why: To know the portion of cases that was the result of each of five gun trafficking violations

How: survey

When: 2000

Where: the U.S. Bureau of Alcohol, Tobacco and Firearms (BATF)

b) What do you notice about the percentages listed? What does that probably mean?

About 46% of illegal gun trafficking is done by Straw purchase.

About 21% of illegal gun trafficking is done by unlicensed sellers.

About 14% of illegal gun trafficking is done through Gun shows and flea markets.

About 14% of illegal gun trafficking cases are gun stolen from federally licensed dealers.

About 14% of illegal gun trafficking cases are gun stolen from residences.

In conclusion, 1 in 2 gun trafficking violations are done by Straw purchase.

6. The Chance article in the winter of 2003 reported on the Houston independent school district’s magnet schools program. Of the 1755 qualified applicants, 931 were accenpted, 298 were saitlisted, and 526 were turned away for lack of space. It also indicated that 517 applicants were black or Hispanic, 292 Asian, and 946 white. Summarize the relative frequency distribution of ethnicity with a sentence or two (in the proper context, of course).

About half of the qualified applicants in the Houston independent school district’s magnet schools program belong to white ethnicity (54%). Besides, black or Hispanic, and Asian qualified applicants are 29 and 17 percent, respectively.

Black or Hispanic = 517/1755 = 0.2946 or 29.46%

Asian = 292/1755 = 0.1664 or 16.64%

White = 946/1755 =0.5390 or 53.90%

7. A survey of autos parked in student and staff lots at a large university classified the brands by country of origin,                Origin/Driver

Student
Staff
American
107
105
European
33
12
Asian
55
47

Student
Staff
Row Total
American
107
105
212
European
33
12
45
Asian
55
47
102
Col Total
195
164
359

Student
Staff
Row Total
American
0.5487
0.6402
0.5905
European
0.1692
0.0732
0.1253
Asian
0.2821
0.2866
0.2841
Col Total
1.0000
1.0000
1.0000
a) What percentage of all the cars surveyed were foreign?

P = (33+12+55+47)/359 = 147/359 = 0.4095 or 40.95%

b) What percentage of the American cars were owned by students?

P = 107/212 = 0.5047 or 50.47%

c) What percentage of the students owned American cars?

P = 107/195 = 0.5487 or 54.87%

d) What is the marginal distribution of origin?

The marginal distribution of origin is 59.05% American, 12.53% European, and 28.41% Asian.

(Highlighted by green)

e) What are the conditional distributions of origin by driver classification?

The conditional distribution of origin by student is 54.87% American, 16.92% European, and 28.21% Asian. The conditional distribution of origin by staff is 64.02% American, 7.32% European, and 28.66% Asian.

(Highlighted by yellow)

8. In 2000 the Journal of the American Medical Association (JAMA) published a study that examined pregnancies that resulted in the birth of twins. Births were classified as preterm with intervention (induced labor or cesarean), preterm without procedures, or term/postterm. Researchers also classified the pregnancies by the level of prenatal medical care the mother received (inadequate, adequate, or intensive). The data, from the years 1995-97, are summarized in a table in the textbook. Figures are in thousands of births. (JAMA 284 [2000]:335-341)  Level of prenatal care/Twin Births 19995-1997(in thousands)

Preterm(induced or ceasarean
Preterm(without procedures)
Term of post-term
TOTAL
Intensive
18
15
28
61
Adequate
46
43
65
154
Inadequate
12
13
38
63
TOTAL
76
71
131
278
a) What percent of these mothers did not receive adequate medical care during their pregnancies?

P = 63/278 = 0.2266 or 22.66% (Taking only case of Inadequate)

b) What percent of all twin births were preterm?

P = (76 + 71)/278 = 147/27 = 0.5288 or 52.88%

c) Among the mothers who did not receive adequate medical care, what percentage of the twin births were preterm?

P = (12 + 13)/63 = 25/63 = 0.3968 or 39.68% (Taking only case of Inadequate)

d) Write a few sentences describing the association between these two variables.

The two variable births and pregnancies are not associated that is independent. The null hypothesis that births is independent of pregnancies is not rejected in Chi-Square Test for Independence, Chi-square(4) = 6.14, p = 0.1887 (> 0.05).

Table : Chi-square Contingency Table Test for Independence

Preterm(induced or ceasarean
Preterm(without procedures)
Term of post-term
Total
Intensive
Observed
18
15
28
61

Expected
16.68
15.58
28.74
61.00

(O – E)² / E
0.11
0.02
0.02
0.15
Adequate
Observed
46
43
65
154

Expected
42.10
39.33
72.57
154.00

(O – E)² / E
0.36
0.34
0.79
1.49
Inadequate
Observed
12
13
38
63

Expected
17.22
16.09
29.69
63.00

(O – E)² / E
1.58
0.59
2.33
4.51
Total
Observed
76
71
131
278

Expected
76.00
71.00
131.00
278.00

(O – E)² / E
2.05
0.96
3.14
6.14
6.14
chi-square
4
df
.1887
p-value
5. The 92 students in a statistics class are classified by gender and by whether or not they smoke. The results are given in the table below. You are interested in the relationship between these two variables. A report on these data concludes that there are 2.5 times as many male smokers as there are female smokers. Why is this conclusion misleading? Perform whatever calculations you feel are necessary to compare the rate at which each gender smoke. Summarize your results in no more than two sentences.

Male
Female
All
Smoker
20
8
28
Non-Smoker
37
28
64
All
57
35
92

The calculation is misleading because the sample population for men and female are not equal. Of 35 female students, only 8 smokes, however of 57 students, only 20 smokes, therefore, the rate at which male smoke is 35.09% and the rate at which female smoke is 22.86%.

Cite this ISQF

ISQF. (2016, Oct 28). Retrieved from https://graduateway.com/isqf/

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