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##### STAT Misc. Problems....mcqs

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Question;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 of0.837tell us about interaction?AnswerThere 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 2What would interaction mean in the context of this analysisAnswerInteraction 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 3The p-value of0.541tells us that?AnswerThere 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 4The p-value of0.000tells us that...AnswerThere 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 5Which comment is correct for the first plot.AnswerThe 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 6Which comment is correct about the second plot?AnswerThe 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 7Data 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?AnswerThere 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 8What does the p-value of 0.217 tell us?AnswerThere 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 pointsQuestion 9What does the p-value of 0.016 tell us?AnswerThere 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 pointsQuestion 10What does the value of R-sq(adj) tell us?AnswerOnly 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 pointsQuestion 11What is the following plot telling us?AnswerThere 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 pointsQuestion 12The 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 10.0AnswerThe 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 pointsQuestion 13A 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, 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 Resid19 3.00 245.00 277.32 3.14 -32.32 -2.26R25 3.00 281.00 310.90 2.80 -29.90 -2.08R60 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...AnswerThere 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 pointsQuestion 14The p-value of 0.000 for km2tpt indicates that...AnswerThere 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 pointsQuestion 15The p-value of 0.148 indicates that...AnswerThere 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 16Which of the following statements is correct regarding the below plots?AnswerThe 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 17Which of these comments is correct regarding the plot below?AnswerThe 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 pointsQuestion 18Approximately how many observations would you expect to be reported with anRbeside them in the Minitab output for this analysis?Answer34560.5 pointsQuestion 19Are any serious concerns raised by the ?Unusual Observations? reported in the output above? Select the most appropriate answer.AnswerYes, 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#61380 | Written in 18-Jul-2015

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