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# Chi square test for Goodness of fit & Association

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(1) Records of randomly selected births were obtained and categorized according to the day of the week that they occurred. 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. Provide an explanation for the result.

DAY SUN MON TUES WED THURS FRI SAT
NUMBERS OF BIRTHS 77 110 124 122 120 123 97

(2) Do World War II Bomb Hits Fit a Poisson Distribution? 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 Poisson 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 227.5 211.4 97.9 30.5 8.7
(from poisson distribution)

(3) In a USA Today article about an experimental nasal spray vaccine for children, the following statement was presented: In a trial involving 1602 children only 14 of the 1070 who received the vaccine developed the flu, compared with 95 of the 532 who got a placebo. 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?

Developed Flu?
Yes No
Vaccine treatment 14 1056

Placebo 95 437

(4) Is seat belt use independent of cigarette smoking? A study of seat-belt users and non-users yielded the randomly selected sample data summarized in the table below. Test the claim that the amount of smoking is independent of seat-belt use. A plausible theory is that people who smoke 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 and over
Wear seat belts 175 20 42 6
Don't wear seat belts 149 17 41 9