MATH2209 Lab 6 No quiz for Lab 6. Please submit answers by uploading a file to Moodle. Question 1 Assume you are doing a test of significance for comparing counts in a two-way contingency table. For the following cases that could arise, look up the P-value as accurately as possible using the appropriate statistical table. Cas e Numbe r of Rows Number of Columns Test Statistic 1 2 2 X2 = 6.498 2 2 4 X2 = 6.498 3 4 2 X2 = 6.498 4 4 5 X2 = 6.498 5 6 8 X2 = 6.498 Degrees of Freedom Value(s) on Table P-value Question 2 A random sample of 150 Introductory Stats students last semester at MSVU were separated based on gender (male or female) and then asked what kind of car they have (domestic, foreign or unknown). Only students who have a car are included here. Type of Car Foreign I don't know Gender Domestic Female 46 49 17 Male 11 24 3 Row Total a. Complete the table above by filling in the row totals. b. For the females in the sample, the distribution of Type of Car is provided. Complete the table below by calculating the distribution of Type of Car for the males. Gender Female Type of car Foreign 49/112 = 43.75% Domestic 46/112 = 41.07% Male I don't know 17/112 = 15.18% Row Total 100% 100% c. For the individuals who are female, the bar chart of the distribution of their Type of Car is provided. For the males, draw a bar chart for the distribution of Type of Car. Make sure to use percentages and use the same scale as the graphs provided to make your comparisons easier. Remember to label your graphs clearly. You need to add the appropriate labels to the graphs that were provided. Be sure to give each chart a title, include variable names, and label both the horizontal and vertical axes. Distribution of Type of Car for Females 70 60 Percent 50 40 30 20 10 0 Domestic Foreign I don't know Type of Car d. Based on the graphs in part (c), what can you say about the association between gender and type of car? Circle one of the following: No association Moderate Association Strong Association e. Explain, with specific reference to the graphs in part (c), your answer to part (d). Determine if the data provide evidence at a 5% significance level that gender is independent of type of car. Use the Minitab Output below to help you answer the following questions. Chi-Square Test for Association: Gender, Type of Car Rows: Gender Columns: Type of Car Domestic Foreign I Dont Know Female 46 42.56 0.2780 49 54.51 0.5563 17 14.93 0.2860 112 Male 11 14.44 0.8195 24 18.49 1.6397 3 5.07 0.8430 38 57 73 20 150 All Cell Contents: All Count Expected count Contribution to Chi-square Pearson Chi-Square = 4.423, DF = 2, P-Value = 0.110 f. On the Minitab output above, circle or highlight the number of female students in the sample who have a domestic car. g. Is this a test of homogeneity or independence? Explain in context. h. The independence assumption is met. Is the expected cell condition met? Explain. i. State the appropriate hypotheses in plain English, in the context of the problem. j. For the female students who said their car is a domestic model, state the expected value and the chi-squared contribution (from the output) and show how each are calculated. Expected Value: __________________ 2 Contribution: _________________ Expected Value Formula Values filled in 2 Contribution Formula Values filled in k. What is the value of the test statistic? _________________ l. Calculate the degrees of freedom and report the P-value from the table in your text AND the output. Degrees of freedom: ______________________ Value(s) from Table: ______________________ P-value from the Table: ____________________ P-value from the output: ____________________ m. Briefly assess the strength and significance of the evidence. Strength: Significance: n. State your conclusion in the context of the problem. Question 3 Turn to page 258 of your textbook and read the story for question 18. For the purpose of this lab, we will be looking at the data for the Australian Crocodiles only. Use the Minitab output, and the graphs provided on the last page of this lab, to answer the following questions. a. Based on the fitted line plot, do you think head size is a good predictor of body length? Explain. b. State the least-squares regression line relating predicted body length and head size. c. Use the regression equation to find the predicted body length, , for observation 9 (the crocodile with a head size of 52 cm). Head size = ___________ Predicted body length = ___________ (Don't forget to state your units.) Circle the predicted value on the output and record it here: ______________ d. Calculate the residual for observation 7 by hand: Residual = ___________ = _____________ (formula) Answer: __________ (calculation) Now circle the residual on the Minitab output. Copy the Minitab value here: ______________ e. The sample slope is __________. Interpret this value in the context of the problem. Minitab Output: Regression Analysis: Body versus Head Analysis of Variance Source Regression Head Error Lack-of-Fit Pure Error Total DF 1 1 13 10 3 14 Adj SS 95610.2 95610.2 1837.2 1589.7 247.5 97447.4 Adj MS 95610.2 95610.2 141.3 159.0 82.5 F-Value 676.54 676.54 P-Value 0.000 0.000 1.93 0.321 Model Summary S 11.8879 R-sq 98.11% R-sq(adj) 97.97% R-sq(pred) 97.45% Coefficients Term Constant Head Coef -21.3 7.828 SE Coef 12.9 0.301 T-Value -1.65 26.01 P-Value 0.123 0.000 Regression Equation Body = -21.3 + 7.828 Head Fits and Diagnostics for All Observations Obs 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Body 161.00 179.00 226.00 259.00 287.00 300.00 342.00 333.00 406.00 459.40 376.20 380.00 265.00 349.00 263.60 Fit 166.52 166.52 229.14 252.62 291.76 291.76 338.73 354.38 385.69 452.23 375.52 397.43 272.98 337.94 272.98 Resid -5.52 12.48 -3.14 6.38 -4.76 8.24 3.27 -21.38 20.31 7.17 0.68 -17.43 -7.98 11.06 -9.38 Std Resid -0.54 1.23 -0.28 0.56 -0.42 0.72 0.29 -1.89 1.84 0.72 0.06 -1.59 -0.70 0.97 -0.82 VIF 1.00 Fitted Line Plot Body = - 21.34 + 7.828 Head 500 S 11.8879 R-Sq 98.1% R-Sq(adj) 98.0% 450 Body 400 350 300 250 200 150 20 30 40 Head 50 60