Activity6-Chi-SquareTests_AnswerSheet (1)

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Feb 20, 2024

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STT 200 – Statistical Methods Fall 2023 Recitation Activity 6 Answer Sheet Chi-Square Distribution and Hypothesis Test Name:__________________________________ Task 1 Responses: 1. ____________________ 2. ____________________ 3. ____________________ Task 2 Responses: Color Observed Count (obs) (count how many of each color are in your sample) Expected Count (exp) Multiply the percentage from the chart above (as a decimal) to your total number of m&ms Contribution (?𝑏𝑠 − 𝑒𝑥?) 2 𝑒𝑥? Brown Yellow Red Blue Orange Green Total Are the conditions met for a chi-square goodness of fit test? Explain with reference to each condition for this test. State the degrees of freedom: _____________________ Calculate the p-value. Show your work by sketching the chi-square curve, shading the area corresponding to the p-value and writing down the command you used in your calculator. Evaluate the compatibility or consistency of the null model (website percentages) with your observed sample data. Bee Miller 0.6321 0.1205 0 Condition 1: each count must be independent of all other cases in the table. variables.) above.)Condition 3: Must be 3 levels to a categorical variable. (There are 6 colors of m&ms, giving us 6 catgorical Condition 2: The expected count for the categorical variable must be at least 5. (It is never below five in the table (Random sampling of m&ms lets us assume idependent observations) 5 x squaredcdf(9.9113,10^10,5) = .0778 There is some evidence against the null model.

STT 200 – Statistical Methods Fall 2023 Recitation Activity 6 Answer Sheet Chi-Square Distribution and Hypothesis Test Task 3 Responses: Step 1: Construct the null and alternative hypotheses. 𝑯 𝟎 : 𝑯 𝒂 : Step 2: Calculate the expected counts for each cell of the table. Mon Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total Expected Counts 119 Step 3: Are the conditions for the test met? Explain how you know. Step 4: Test statistic 𝜒 2 = _______________ Step 5: Degrees of freedom = _______________ Step 6: Calculate and interpret the p-value. Proportion of cats falling from new york buildings is the same across all months of the year. Proportion of cats falling from new york buildings is different across all months of the year. 9.917 9.917 9.917 9.917 9.917 9.917 9.917 9.917 9.917 9.9179.917 9.917 ex[ected count in each cell is higher than 5. Yes, there are at least 12 categorical variables, the cats will be independent of each other, and the 20.6632 11 0.037There is strong evidence against the null model.

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Activity6-Chi-SquareTests_AnswerSheet (1)

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