# STATS Quiz 4 Multiple Choice Questions

Question 1The following output is based on data from the foam height investigation of Quiz 2. Use the information in this output to answer Questions 1 to 6.Two-way ANOVA: foam ht versus glass temp, angleSource DF SS MS F Pglass temp 1 40.11 40.11 0.38 0.541angle 2 2310.89 1155.44 11.00 0.000Interaction 2 37.56 18.78 0.18 0.837Error 30 3151.67 105.06Total 35 5540.22(Bartlett’s Test: Test Statistic = 2.21, p-value = 0.820)(Levene’s Test: Test Statistic = 1.21. p-value = 0.328)What does the p-value of 0.837 tell us about interaction?Answer There is very strong evidence of interaction. There is no/insufficient interaction. There is some evidence of interaction. There is no evidence that average foam height differs for different glass temperature (allowing for the effect of pouring angle)Question 21. What would interaction mean in the context of this analysisAnswer Interaction means that the effect of pouring angle differs for different glass temperatures. Interaction means that the effect of foam height differs for different glass temperatures. Interaction means that the effect of pouring angle differs for different foam heights. Interaction means that when people drink together they engage in conversation.1 points Question 31. The p-value of 0.541 tells us that…Answer There is very strong evidence that average foam height differs for different glass temperatures (allowing for the effect of pouring angle). There is some evidence that average foam height differs for different glass temperatures (allowing for the effect of pouring angle). There is no evidence that average foam height differs for different pouring angle (allowing for the effect of glass temperatures) There is no evidence that average foam height differs for different glass temperatures (allowing for the effect of pouring angle)1.5 points Question 41. The p-value of 0.000 tells us that …Answer There is extremely strong evidence that average foam height differs for different pouring angles (allowing for the effect of glass temperature). There is some evidence that average foam height differs for different pouring angles (allowing for the effect of glass temperature). There is insufficient evidence that average foam height differs for different glass temperature (allowing for the effect of pouring angles). There is extremely strong evidence that average foam height differs for different glass temperature (allowing for the effect of pouring angles). 1.5 points Question 51. Which comment is correct for the first plot.Answer The assumption of equal variance (for all combinations on the factor categories) is not reasonable. The assumption of equal variance (for all combinations on the factor categories) is reasonable. The plot is reasonably straight, so the assumption that foam heights are normally distributed about their location mean (or within each combination of categories) is reasonable. The plot is curved, so the assumption that foam heights are normally distributed about their location mean (or within each combination of categories) is not reasonable. 1 points Question 61. Which comment is correct about the second plot?Answer The assumption of equal variance (for all combinations of the factor categories) is not reasonable. The assumption of equal variance (for all combinations of the factor categories) is reasonable. The plot is reasonably straight, so the assumption that foam heights are normally distributed about their local means (or within each combination of categories) is reasonable. The plot is curved, so the assumption that foam heights are normally distributed about their local means (or within each combination of categories) is not reasonable.1 points Question 71. Data was gathered on spatial perception by asking their subjects to estimate either or both of a 5cm length and a 10cm length. They also recorded the subject’s gender, age range (in decades: 10–19, 20–29, 30–39, 40–49) and whether they were right-handed or left-handed. The following analyses are based on this data set.The following output relates to the estimates for the 10cm length. Use the information in this output to answer Questions 7 to 11.General Linear Model: Estimate of versus Left/Right H, Age_group_10Analysis of Variance for Estimate of Length(cm)_10, using Adjusted SS for TestsSource DF Seq SS Adj SS Adj MS F PLeft/Right Handed_10 1 0.862 0.155 0.155 0.02 0.887Age_group_10 3 6.962 34.895 11.632 1.53 0.217Left/Right Handed_10*Age_group_10 3 85.213 85.213 28.404 3.73 0.016Error 57 434.326 434.326 7.620Total 64 527.362S = 2.76039 R-Sq = 17.64% R-Sq(adj) = 7.53% What does the p-value of 0.887 tell us?Answer There is strong evidence of interaction (i.e. that the differences between average lengths) estimated by the various age groups are different for right and left handed people). There is no evidence of any difference in average length estimated by different age groups, averaged over handedness. There is no evidence of any difference in average length estimated by left and right handed people, averaged over age groups. There is strong evidence of a linear relationship between age and estimated length.1.5 points Question 81. What does the p-value of 0.217 tell us?Answer There is strong evidence of interaction (i.e. that the differences between average lengths) estimated by the various age groups are different for right and left handed people). There is no evidence of any difference in average length estimated by different age groups, averaged over handedness. There is no evidence of any difference in average length estimated by left and right handed people, averaged over age groups. There is strong evidence of a linear relationship between age and estimated length.1.5 points Question 91. What does the p-value of 0.016 tell us?Answer There is strong evidence of interaction (i.e. that the differences between average lengths) estimated by the various age groups are different for right and left handed people). There is no evidence of any difference in average length estimated by different age groups, averaged over handedness. There is no evidence of any difference in average length estimated by left and right handed people, averaged over age groups. There is strong evidence of a linear relationship between age and estimated length.1.5 points Question 101. What does the value of R-sq(adj) tell us?Answer Only 7.5% of the variation in estimated lengths has been explained by fitting this model. Only 17.6% of the variation in estimated lengths has been explained by fitting this model. Only 7.5% of the variation in estimated lengths has been explained by fitting this model, adjusted for the number of terms in the model. Only 17.6% of the variation in estimated lengths has been explained by fitting this model, adjusted for the number of terms in the model.1.5 points Question 111. What is the following plot telling us? Answer There is no interaction. The effects are acting additively. Left handed people tend to estimate greater lengths than right handed people for the 10-19, 30-39 and 40-49 year age group, but strongly the other way around for the 20-29 year age group. Right handed people tend to estimate greater lengths than left handed people for the 10-19, 30-39 and 40-49 year age group, but strongly the other way around for the 20-29 year age group.1.5 points Question 121. The following output was obtained from an analysis comparing estimates for 5cm across age groups and genders. What does the output tell us?Tukey 95.0% Simultaneous Confidence IntervalsAll Pairwise Comparisons among Levels of Age_group_5Age_group_5 = 10-19 subtracted from:Age_group_5 Lower Center Upper —–+———+———+———+-20-29 0.232 3.539 6.846 (——*——)30-39 -2.525 2.911 8.347 (———-*———-)40-49 -2.599 1.446 5.492 (——-*——-) —–+———+———+———+- -5.0 0.0 5.0 10.0Age_group_5 = 20-29 subtracted from:Age_group_5 Lower Center Upper —–+———+———+———+-30-39 -6.160 -0.628 4.903 (———-*———-)40-49 -6.266 -2.093 2.081 (——–*——-) —–+———+———+———+- -5.0 0.0 5.0 10.0Age_group_5 = 30-39 subtracted from:Age_group_5 Lower Center Upper —–+———+———+———+-40-49 -7.467 -1.464 4.538 (———–*———–) —–+———+———+———+- -5.0 0.0 5.0 10.0Answer The only age groups with clear evidence of a difference in average estimates for the 5cm length were the 10-19 and 20-29 age groups. The only age groups without clear evidence of a difference in average estimates for the 5cm length were the 10-19 and 20-29 age groups. There is strong evidence of a difference in average estimates for all of the age groups. There is no evidence of a difference in average estimates for any of the age groups. 2 points Question 131. A study of rental prices for houses considered the effects of distance from public transport (km2tpt), number of bedrooms (b-rms) and letting agent (agentA). In the area being studied, the two largest letting agents accounted for the majority of rentals, so the analysis was initially restricted to these two agents only. Note that the variable agentA takes the values 1 for houses let through agent A and 0 for those let through agent B.The data obtained from this study were entered into Minitab, and the following printout was obtained as part of the analysis. Use the information in this printout to answer Questions 13 to 19.1. Regression Analysis: rent$ versus b-rms, km2tpt, agentAThe regression equation isrent$ = 165 + 55.0 b-rms – 33.9 km2tpt + 5.23 agentAPredictor Coef SE Coef T PConstant 164.999 6.195 26.64 0.000b-rms 54.967 1.832 30.00 0.000km2tpt -33.926 2.899 -11.70 0.000agentA 5.234 3.583 1.46 0.148S = 14.6181 R-Sq = 94.3% R-Sq(adj) = 94.1%Analysis of VarianceSource DF SS MS F PRegression 3 259042 86347 404.08 0.000Residual Error 73 15599 214Total 76 274641Unusual ObservationsObs b-rms rent$ Fit SE Fit Residual St Resid 19 3.00 245.00 277.32 3.14 -32.32 -2.26R 25 3.00 281.00 310.90 2.80 -29.90 -2.08R 60 3.00 265.00 294.08 2.29 -29.08 -2.01RR denotes an observation with a large standardized residualThe p-value of 0.000 for b-rms indicates that …Answer There is extremely strong evidence that the number of bedrooms affects the average rental price in a linear fashion, after allowing for the other predictors. There is extremely strong evidence that distance to transport affects the average rental price in a linear fashion, after allowing for the other predictors. There is no evidence that letting agent affects the average rental price in a linear fashion, after allowing for the other predictors. The model fits the data well.1.5 points Question 141. The p-value of 0.000 for km2tpt indicates that …Answer There is extremely strong evidence that the number of bedrooms affects the average rental price in a linear fashion, after allowing for the other predictors. There is extremely strong evidence that distance to transport affects the average rental price in a linear fashion, after allowing for the other predictors. There is no evidence that letting agent affects the average rental price in a linear fashion, after allowing for the other predictors. The model fits the data well.1.5 points Question 151. The p-value of 0.148 indicates that …Answer There is extremely strong evidence that the number of bedrooms affects the average rental price in a linear fashion, after allowing for the other predictors. There is extremely strong evidence that distance to transport affects the average rental price in a linear fashion, after allowing for the other predictors. There is no evidence that letting agent affects the average rental price in a linear fashion, after allowing for the other predictors. The model fits the data well.Question 161. Which of the following statements is correct regarding the below plots? Answer The assumption that rental prices are normally distributed about the average for the relevant predictor values appears to be reasonable. There is no indication of a non-linear trend for rental prices against distance to transport, and the variance appears to be fairly consistent. The variance appears very different for the two agents. There is an indication of a quadratic trend for rental prices against distance to transport, and the variance appears to be fairly consistent. The variance appears fairly consistent for the two agents. There is no indication of a non-linear trend for rental prices against distance to transport, and the variance appears to be fairly consistent. The variance appears fairly consistent for the two agents.Question 171. Which of these comments is correct regarding the plot below?1. Answer The assumption that rental prices are normally distributed about the average for the relevant predictor values appears to be reasonable. There is no indication of a non-linear trend for rental prices against distance to transport, and the variance appears to be fairly consistent. The variance appears very different for the two agents. There is an indication of a quadratic trend for rental prices against distance to transport, and the variance appears to be fairly consistent. The variance appears fairly consistent for the two agents. There is no indication of a non-linear trend for rental prices against distance to transport, and the variance appears to be fairly consistent. The variance appears fairly consistent for the two agents.1 points Question 181. Approximately how many observations would you expect to be reported with an R beside them in the Minitab output for this analysis?Answer 3 4 5 60.5 points Question 191. Are any serious concerns raised by the “Unusual Observations” reported in the output above? Select the most appropriate answer.Answer Yes, we don’t want any unusual observations. Yes, we only want one unusual observation per data set. Not really – there are less than the expected number calculated above. Not really – there are more than the expected number calculated above.

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