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Question: worksheet chi square and correlation suppose we have three categories...

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Worksheet: Chi Square and Correlation Suppose we have three categories A, B, and C. Assume that the historical distribution of observations among these four categories is 20%, 40%, and 40% respectively. A sample of size 250 is taken, and we find 75 observations in category A, 125 in category B, and 50 in category C 1. a. State the null hypothesis for the Chi-square goodness-of-fit test. b. What are the expected frequencies for each category? c. Calculate the χ 2 statistic. d. e. Calculate the standardized residual for category A f. Calculate the standardized residual for category B. State your conclusion at α-.05. g. Calculate the standardized residual for category C h. What do the standardized residuals tell us? 2. Suppose we have four categories A, B, C and D. Assume that the percentage of observations in each category is equal. A sample of size 500 is taken, and we find 100 in category A, 100 in category B, 140 in category C and 160 in category D. a. Which Chi-square test is appropriate in this situation? Explain. . What are the expected frequencies for each category? c. Calculate the x 2 statistic. State your conclusion at α-.01. 3. A survey about Internet usage included the following question Do you bank online? The data are shown below for adults under the age of 25 broken down by gender. Is the proportion of who banks online the same for men and women? Men 188 112 300 Total 363 237 600 Bank online? Women Yes 175 125 300 No Total a. What is the point estimate for the difference between the proportions. b. Calculate the x 2 statistic to determine whether the proportions are equal. State your conclusion at α = .05. c. Provide a 95% confidence interval for the difference between the proportions. Is this consistent with your conclusion above?
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