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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

https://brainmass.com/math/probability/chi-square-test-goodness-fit-association-440385

#### Solution Summary

The solution provides step by step method for the calculation of chi square test for goodness of fit and association. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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## Statistics: Entrances to Government building; mail order sales; job pressure vs age

20. There are four entrances to the Government Center Building in downtown Philadelphia. The building maintenance supervisor would like to know if the entrances are equally utilized. To investigate, 400 people were observed entering the building. The number using each entrance is reported below. At the .01 significance level, is there a difference in the use of the four entrances.

Entrance Frequency
Main Street 140
Cherry Street 90
Walnut Street 50
Total 400

21. At the .01 significance level, does the distribution of the orders reflect the population?

The owner of a mail-order catalog would like to compare her sales with the geographic distribution of the population. According to the United States Bureau of the Census, 21 percent of the population lives in the Northeast, 24 percent in the Midwest, 35 percent in the South, and 20 percent in the West. Listed below is a breakdown of a sample of 400 orders randomly selected from those shipped last month. At the .01 significance level, does the distribution of the orders reflect the population?

Region Frequency
Northeast 68
Midwest 104
South 155
West 73
Total 400

26. Relationship between job pressure and age

A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the .01 significance level, is there a relationship between job pressure and age?

Degree of Job Pressure
Age (years) Low Medium High
Less than 25 20 18 22
25 up to 40 50 46 44
40 up to 60 58 63 59
60 and older 34 43 43

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A sample of employees at a large chemical plant was asked to indicate a preference for one of three pension plans.

A sample of employees at a large chemical plant was asked to indicate a preference for one of three pension plans. The results are given in the following table. Does it seem that there is a relationship between the pension plan selected and the job classification of the employees? Use the .01 significance level.

? Pension Plan

Job Class Plan A Plan B Plan C
Supervisor 10 13 29
Clerical 19 80 19
Labor 81 57 22

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