4) A test that Species is not needed in the model, given that Thickness is in the model, can be conducted as a joint test that two model parameters are both equal to 0. For this test, specify the model equation and the appropriate null and alternative hypotheses. Obtain the value of the F test statistic and state the degrees of freedom associated with the F test statistic.

5) The p-value for the value of the F test statistic that you should have calculated in question 4 is 0.38 (there is no way for you to verify this without a computer). What does this p- value allow us to conclude regarding the hypothesis test in question 4?

6) Someone claims that starch films made from potatoes are stronger than those made from corn. Is this a reasonable claim?

R Output for Questions 4-7 (the "Starch Film" Data Set) > FilmMod2 summary (FilmMod2) Call : Im (formula = BreakingStrength ~ Thickness + Species + Thickness: Species) Residuals : Min 10 Median 30 Max -261.79 -121.00 -57. 85 80 . 95 604.89 Coefficients: Estimate Std. Error t value Pr (>It|) (Intercept) -39.90 215.06 -0.186 0. 8546 Thickness 76.68 29. 62 2.589 0. 0171 SpeciesPotato 420 .85 536. 89 0. 784 0. 4419 Thickness : SpeciesPotato -23.60 51. 84 -0. 455 0. 6536 Signif. codes: ( * ** */ 0. 001 .#*# 0.01 * * 0. 05 . . ' 0.1 . ' 1 Residual standard error: 209.2 on 21 degrees of freedom Multiple R-squared: 0. 672, Adjusted R-squared: 0.6251 F-statistic: 14.34 on 3 and 21 DF, p-value: 2.616e-05 > anova (FilmMod2) Analysis of Variance Table Response: BreakingStrength Df Sum Sq Mean Sq F value Pr (>F) Thickness 1 1795180 1795180 41. 0105 2.391e-06 * * * Species 1 78985 78985 1 . 8044 0.1935 Thickness : Species 9070 9070 0.2072 0.6536 Residuals 21 919247 43774 Signif. codes: 0 ' ** *' 0.001 #*' 0.01 . * 0.05 . . ' 0.1 ' ' 1> plot (Thickness, BreakingStrength, pch= c("C", "P") [unclass (Species)]) P P P Breaking Strength 400 600 800 1000 1200 1400 1600 P Pp P C C P P P C C P C P & 6 C 6 co 10 12 Thickness 14