Assignment - Cross-tabulation and Chi-square
Q1. With an ex post facto bivariate cross-sectional design, researchers have analyzed the relationship between college students' country of origin and whether they have purchased a good via e-commerce. The data were collected via a disproportionate stratified random sample of college students at a U.S. university.
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Native U.S. college students
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International U.S. college students
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Have purchased good via e-commerce
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54
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23
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Have not purchased good via e-commerce
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36
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67
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a. The cell frequencies are shown above. Calculate and show (in the table) the row and column marginals (both frequencies and percentages), the total sample size, and for each cell the expected frequency.
b. State the null hypothesis to be tested by a crosstabulation and chi-square analysis.
c. Why do you suppose the researchers chose a disproportionate stratified random sample in this study?
d. Given the level of significance of .05 and degree of freedom, find out the significant χ2 value. Calculate the test statistics and decide whether the researchers should reject the null hypothesis, and interpret the result.
e. Graph the relationship with a bar graph.
Q2. A researcher using the 2002 Survey of Consumer Finances cross-sectional data (n=4,299) have investigated the relationship between whether or not a household has credit cards and whether the marital status of the head of household is married or not married. Suppose that the researcher has decided the level of significance is .001 and the calculated chi-square is 144.53 with a p-value of .00024. Suppose that the Phi coefficient regarding the relationship between the variables is calculated to be .06. Discuss (a) the statistical significance of the tested relationship and (b) the strength (or practical significance) of the relationship.
Q3. A researcher wishes to analyze the null hypothesis: there is no statistically significant relationship between recent homebuyers' willingness-to-pay for universal design features in housing and whether they bought a single-family home or condominium housing. She collects data from a simple random sample of 100 recent homebuyers, 81 of whom purchased single-family houses and 19 of whom purchased condos. She measured willingness-to-pay for universal design features in housing with a scale with the unit of measurement in percentages, She found that 41 homebuyers were willing to pay no more (0%) for the features, 29 homebuyers were willing to pay between 0.10% to 4.99% more for the features, 24 homebuyers were willing to pay between 5.00% and 9.99% more and six homebuyers were willing to pay 10% or greater more for the universal design features. She thinks that she may have a problem implementing a chi-square analysis to test her hypothesis. Does she? If so, what is the problem? How could she fix the problem and test her hypothesis with the data?