Preferences for the type of diet drink from a random sample of 121 shoppers are in the table below. A researcher is interested in determining if there is a relationship between the type of diet drink preferred and the age of the shoppers. Perform categorical data analysis using alpha = .05. Be sure to clearly state your hypotheses, decision and conclusion. Diet Pepsi Diet Coke Diet Sprite Under 25 25 and Years Old Older 10 60 18 14 9 10 Problem #2 A proofreader checked 160 documents for grammatical errors. The distribution obtained is shown below. At alpha= .01, perform a chi-square test of proportions to see whether this sample came from a uniform distribution. Be sure to clearly state your hypotheses, decision and conclusion. Number Observedof errors frequency 0 10 1 65 Problem #3 An automobile insurance company collected 24 months of data to develop a regression model to predict collision claims as a function of the percentage of drivers under age 30 and average temperature. Use the data in the table below to perform the analysis. a) Describe the relationships between the independent and dependent variables suggested by the scatterplots. b) Write the equation for this multiple regression model. c) Formally test the global usefulness of the model using alpha = .05. Interpret the result in practical terms. d) Test the temperature coefficient using alpha = .05. Interpret the result in practical terms. e) What information about this model does the coefficient of multiple determination provide? f) Perform residual analysis to check the regression assumptions. g) Predict, with 95% confidence, the collision claim amount for a month with an average temperature of 29F and with 60% of claims by drivers under age 30. Collision Claim Pct Under Temp ($) 30 (%) (F) 116250 50 31.5 217180 60.8 33 43436 45.1 45 159265 56.4 53.9 130308 53.3 63.9 72393 46.9 74.5 174740 57.8 79.4 101351 50.6 75.3 144787 55 68.7 28957 35.8 53.7 173744 57.9 47.6 86872 49.9 38.4 108420 51 28.7 203288 62.9 34.4 40658 45.1 43.9 149078 55.2 51.1 121973 53.7 63.4 67763 47.2 73 163130 56.1 80.5 94858 48.3 79.8 135525 54.7 68 27105 45.4 52.6 162631 56.5 48.9 81315 47.7 35.5 2 71 3 14