12) Records of randomly selected births were obtained and categorized according to the day of the week that they occurred (based on data from the National Center for Health Statistics). Because babies are unfamiliar with our schedule of weekdays, a reasonable claim is that births occur on the different days with equal frequency. Use a 0.01 significance level to test that claim. Can provide an explanation for the result?
|
Day
|
Sun
|
Mon
|
Tues
|
Wed
|
Thurs
|
Fri
|
Sat
|
|
Number of births
|
77
|
110
|
124
|
122
|
120
|
123
|
97
|
18) In analyzing hits by V-1 buzz bombs in World War II, South London was subdivided into regions, each with an area of 0.25 km2. Shown below is a table of actual frequencies of hits and the frequencies expected with the Poisson distribution. Use the values listed and a 0.05 significance level to test the claim that the actual frequencies fit a Poison distribution.
|
Number of bomb hits
|
0
|
1
|
2
|
3
|
4 or more
|
|
Actual number of regions
|
229
|
211
|
93
|
35
|
8
|
|
Expected number of regions (from Poisson distribution)
|
227.5
|
211.4
|
97.9
|
30.5
|
8.7
|
14) In a USA Today article about an experimental vaccine for children, the following statement was presented: “in a trial involving 1602 children, only 14 (1%) of the 1070 who received the vaccine developed the flu, compared with 95 (18%) of the 5632 who got a placebo.” The data are shown in the table below. Use a 0.05 significance level to test for independence between the variable of treatment (vaccine or placebo) and the variable representing flu (developed flu, did not develop flu). Does the vaccine appear to be effective?
|
|
Develop Flu?
|
|
|
Yes
|
No
|
|
Vaccine Treatment
|
14
|
1056
|
|
Placebo
|
95
|
437
|
20) Is Seat Belt Use Independent of Cigarette Smoking? A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the given table (based on data from “What Kinds of People Do Not Use Seat Belts?” by Helsing and Comstock, American Journal of Public Health, Vol. 67, No. 11). Test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke more are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample data?
|
|
Number of Cigarettes Smoked per Day
|
|
|
0
|
1-14
|
15-34
|
35 or over
|
|
Wear seat belts
|
175
|
20
|
42
|
6
|
|
Don’t wear seat belts
|
149
|
17
|
41
|
9
|
18) In the article “Eradication of Small Intestinal Bacterial Overgrowth Reduces Symptoms of Irritable Bowel Syndrome” (Pimentel, Chow, and Lin, American Journal of Gastroenterology, Vol. 95, No.12), the authors include a discussion of whether antibiotic treatment of bacteria overgrowth reduces intestinal complaints. McNemar’s test was used to analyze results for those subjects with eradication of bacterial overgrowth. Using the data in the given table, does the treatment appear to be effective against abdominal pain?
|
|
|
Abdominal Pain Before Treatment?
|
|
|
|
Yes
|
No
|
|
Abdominal pain after treatment?
|
Yes
|
11
|
1
|
|
No
|
14
|
3
|
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