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##### STATS Quiz 4 Questions

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Question;Question 1;The 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, angle;Source DF SS MS F P;glass;temp 1 40.11 40.11 0.38 0.541;angle 2 2310.89 1155.44 11.00 0.000;Interaction 2 37.56 18.78 0.18 0.837;Error 30 3151.67 105.06;Total 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 of0.837tell 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);We reject the null;hypothesis if p-value is small (smaller than significance level). The p-value;0.837 tells us that we can?t reject the null hypothesis for the interaction. As;the null hypothesis is interaction = 0 so p-value =0.837 gives the selected;interpretation.;Question 2;What would interaction mean in the context of this;analysis;Answer;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.;The;variables of consideration are angle and glass temperature and interaction term;means the relation between them thus the answer.;Question 3;The p-value of0.541tells 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);As;p value is larger so we fail to reject the null hypothesis of insignificance;and thus there is no significance for the considered variable which is glass;temperature.;Question 4;The p-value of0.000tells 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).;P-value;is 0 suggesting rejection of null hypothesis i.e. the considered variable is;significant and the considered variables for whose p-value we are considering;is angle so the answer.;Question 5;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.;As;each confidence interval is overlapped hence the answer.;Question 6;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.;As;it?s the Normal probability plot and the dots are almost on the lines hence the;answer.;Question 7;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_10;Analysis of Variance for Estimate of Length(cm)_10;using Adjusted SS for Tests;Source DF Seq SS Adj SS Adj;MS F P;Left/Right;Handed_10 1 0.862 0.155 0.155 0.02 0.887;Age_group_10 3 6.962 34.895 11.632 1.53 0.217;Left/Right;Handed_10*Age_group_10 3 85.213 85.213 28.404 3.73 0.016;Error 57 434.326 434.326 7.620;Total 64 527.362;S = 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.;By;using the same logic as before.;Question 8;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 9;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 10;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 11;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 12;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 Intervals;All Pairwise Comparisons among Levels of;Age_group_5;Age_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 10.0;Age_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 10.0;Age_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 10.0;Answer;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 13;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 variableagentAtakes 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;agentA;The regression equation is;rent$ = 165 + 55.0 b-rms - 33.9 km2tpt + 5.23;agentA;Predictor Coef SE Coef T P;Constant 164.999 6.195 26.64 0.000;b-rms 54.967 1.832 30.00 0.000;km2tpt -33.926 2.899 -11.70 0.000;agentA 5.234 3.583 1.46 0.148;S = 14.6181 R-Sq = 94.3% R-Sq(adj) =;94.1%;Analysis of Variance;Source DF SS MS F P;Regression 3 259042 86347 404.08 0.000;Residual Error 73 15599 214;Total 76 274641;Unusual Observations;Obs 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 -2.01R;R denotes an observation with a;large standardized residual;The 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 14;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 15;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 16;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 17;Which of these comments is correct regarding;the plot below?;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 18;Approximately;how many observations would you expect to be reported with anRbeside;them in the Minitab output for this analysis?;Answer;3;4;5;6;0.5 points;Question 19;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.

Paper#61367 | Written in 18-Jul-2015

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