Discuss the use of two-way tables in general and relate to the results obtained for the HMO study using proportions.

    Discuss the use of two-way tables in general and relate to the results obtained for the HMO study using proportions. The HMO study is repeated here for reference.

    A study was designed to find reasons why patients leave a health maintenance organization (HMO). Patients were classified as to whether or not they had filed a complaint with the HMO. We want to compare the proportion of complainers who leave the HMO with the proportion of those who do not file complaints but who also leave the HMO. In the year of the study, 639 patients filed complaints, and 54 of these patients left the HMO voluntarily. For comparison, the HMO chose an SRS of 743 patients who had not filed complaints. Twenty-two of these patients left voluntarily. Previously we looked at this business problem using proportions. Discuss how to use the Chi-squared distribution and present specific results comparing to the results obtained using proportions.

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    Case study:

    To design effective marketing strategy you need to know your customers. What are the characteristics of people who use the World Wide Web to collect information on travel, and how do they differ from those who do not and use other sources? A survey that collected data to address this question examined the responses of 1401 Web users (WWW) and 1080 people who used other sources for this information (no, other category).The following tables (Week06CaseStudy.xls) give counts of WWW (WWW Yes) and Other (WWW no) for various demographic characteristics. Note that the marginal sums are sometimes less than 1401 and 1080 because of missing data. Use the methods of this chapter to compare the two groups (WWW Yes and Other, WWW No). Include graphical and numerical summaries along with the results of your significance tests. In some cases you may want to combine some categories for the demographic variables. Be sure to include a discussion of missing values. Write a report summarizing your work.

     

    Construct a two-way table based on a business problem statement giving observed counts.
    Determine the applicable degrees of freedom for the model.
    Compute the expected counts for the two-way table.
    Compute the chi-square test statistic for the two-way table.
    Use the chi-square distribution for hypothesis testing involving categorical variables.
    Compute the observed level of significance (p-value) based on the computed chi-square test statistic.
    Based on your statistical analysis results, be able to prepare a business report presenting the conclusions of the analysis.

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    Available data by demographic category in file Week06CaseStudy.xls covers:

    • Age in years.

    • Gender.

    • Education.

    • Occupational category.

    • Household income (U.S. $).

    • Race.

    Age WWWUserA CountA
    Under18 Yes 22
    18to25 Yes 160
    26to35 Yes 328
    36to45 Yes 277
    46to55 Yes 224
    Over55 Yes 101
    Under18 No 24
    18to25 No 161
    26to35 No 184
    36to45 No 189
    46to55 No 164
    Over55 No 109
    Gender WWWUserB CountB
    Female Yes 709
    Male Yes 423
    Female No 561
    Male No 291
    Education WWWUserC CountC
    Grammar Yes 4
    HighSchool Yes 85
    Vocational Yes 54
    SomeCollege Yes 336
    College Yes 357
    PostGrad Yes 259
    Professional Yes 27
    Other Yes 10
    Grammar No 15
    HighSchool No 125
    Vocational No 53
    SomeCollege No 293
    College No 218
    PostGrad No 114
    Professional No 17
    Other No 17
    Occupation WWWUserD CountD
    Mgmt Yes 167
    Prof Yes 264
    Educ Yes 175
    Computer Yes 309
    Other Yes 217
    Mgmt No 87
    Prof No 156
    Educ No 164
    Computer No 164
    Other No 281

    Income WWWUserE CountE

    Lt10K Yes 43
    10to20K Yes 58
    20to30K Yes 116
    30to40K Yes 149
    40to50K Yes 127
    50to75K Yes 259
    75to100K Yes 119
    Over100K Yes 134
    NoAnswer Yes 127
    Lt10K No 65
    10to20K No 78
    20to30K No 102
    30to40K No 127
    40to50K No 105
    50to75K No 129
    75to100K No 71
    Over100K No 47
    NoAnswer No 128
    Race WWWUserF CountF
    Cauc Yes 1001
    Afr Yes 20
    Asian Yes 35
    Hisp Yes 20
    Other Yes 56
    Cauc No 772
    Afr No 16
    Asian No 16
    Hisp No 15
    Other No33

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