{"id":5528,"date":"2022-09-21T11:18:09","date_gmt":"2022-09-21T11:18:09","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5528"},"modified":"2022-10-11T19:46:06","modified_gmt":"2022-10-11T19:46:06","slug":"16b-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/16b-preview\/","title":{"raw":"16B Preview","rendered":"16B Preview"},"content":{"raw":"
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Preparing for the next classIn the next in-class activity, you will need to use an ANOVA table to organize sums of squares and calculate an F-statistic, interpret the coefficient of determination (\ud835\udc452<\/sup>) in context, and use appropriate symbols to represent sample means, actual values, and predicted values.<\/div>\r\n
Questions 1 and 2: Concentration is a memory game in which cards are laid face down on a table and two cards are flipped face up during each turn.The object of the game is to turn over matching pairs of cards. An online version of this game includes three different sets of cards: one has images of animals on the cards, one has images of babies, and one has images of holiday scenes.Are these three versions equally difficult? To investigate, a teacher randomly assigned her students to three groups and each group played a different version of the game. They recorded the amount of time (in seconds) it took to complete the game.The DCMP One-way ANOVA tool at https:\/\/dcmathpathways.shinyapps.io\/ANOVA\/wasused to create the following partially filled-in ANOVA table.<\/div>\r\n<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Source<\/td>\r\nDf<\/td>\r\nSum sq<\/td>\r\nMean sq<\/td>\r\nF value<\/td>\r\n<\/tr>\r\n
Group<\/td>\r\n2<\/td>\r\n177.4<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Error<\/td>\r\n27<\/td>\r\n5715.0<\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Total<\/strong><\/td>\r\n29<\/strong><\/td>\r\n5892.4<\/strong><\/td>\r\n<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
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Question 1<\/h3>\r\n
1) Which of the following is an appropriate description of the variability in this dataset?<\/div>\r\n
a) The amount of variation between the groups (the differences between the versions)is large relative to the amount of variationwithin the groups (the differences between the individual student performances).<\/div>\r\n
b) The amount ofvariation between the groups (the differences between the versions)is small relative to the amount of variationwithin the groups (the differences between the individual student performances).<\/div>\r\n
Hint: Look back at Preview Assignmentand In-Class Activity 14.A to see which sum of squares measures between-groups variabilityand which sum of squares measures within-groups variability.<\/div>\r\n<\/div>\r\n<\/div>\r\n
<\/div>\r\n
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\r\n

Question 2<\/h3>\r\n
\r\n
2) Usethe informationin the ANOVA table to determine if there is evidence that the mean time to complete the game is not the same for all threeversions.<\/div>\r\n
Hint: You may want to fill out the rest of the ANOVA table to keep your information organized. Look back at Preview Assignment 14.B to see how to conduct a one-way ANOVA F-test.<\/div>\r\n<\/div>\r\n
\r\n
Part A: Calculate the F-statistic. Round your answer to fourdecimal places.<\/div>\r\n
Part B: Using your answer from Part A and the FDistribution tool(i.e., data analysis tool), calculate the P-valueathttps:\/\/dcmathpathways.shinyapps.io\/FDist\/.Express your answer as a proportion and round to four decimal places.<\/div>\r\n
Part C:Based on your answer from Part B, which of the following is an appropriate conclusion?<\/div>\r\n
a) Thesedata provide strong evidence to suggest that the mean timesto completethe gamefor all three versions are equal.<\/div>\r\n
b) Thesedata provide strong evidence to suggest that the mean timesto completethe gamefor all three versions are different from eachother.<\/div>\r\n
c) Thesedata provide strong evidence to suggest that a mean time to complete the game for at least one version is different from the others.<\/div>\r\n
d) Thesedata do not provide sufficient evidence to decide whether themean timesto completethe gameforall three versions are different.<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
Questions 3\u20135: Sample data were used to fit a linear regression model that could be used to predict the prices of used cars based on the cars\u2019 mileage.<\/div>\r\n
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\r\n

Question 3<\/h3>\r\n
3) The coefficient of determination (\ud835\udc452) for this model was 0.628. Which of the following is an appropriate interpretation of this value?<\/div>\r\n
a) In this sample, 62.8% of the variation in car prices was explained by the linear regression model using mileage as a predictor.<\/div>\r\n
b) In this sample, 62.8% of the variation in car prices remained unexplained after using the linear regression model with mileage as a predictor.<\/div>\r\n
c) In this sample, 62.8% of the car prices were on the regression line. In other words, the model correctly predicted the prices of 62.8% of the cars.<\/div>\r\n
d)In this sample, 62.8% of the car prices were not on the regression line. In other words, the model incorrectly predicted the prices of 62.8% of the cars.<\/div>\r\n
Hint: Look back at In-Class Activity 6.Cto review the interpretation of the coefficient of determination.<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 4<\/h3>\r\n
4) Which of the following symbols would be used to represent thepredicted price of a car?a)\ud835\udc66b)\ud835\udc66\u0305c)\ud835\udc66\u03025)Which of the following symbols would be used to represent the mean price of all the cars in the dataset?<\/div>\r\n
a) \ud835\udc66<\/div>\r\n
b) \ud835\udc66\u0305<\/div>\r\n
c) \ud835\udc66<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n
Preparing for the next classIn the next in-class activity, you will need to use an ANOVA table to organize sums of squares and calculate an F-statistic, interpret the coefficient of determination (\ud835\udc452<\/sup>) in context, and use appropriate symbols to represent sample means, actual values, and predicted values.<\/div>\n
Questions 1 and 2: Concentration is a memory game in which cards are laid face down on a table and two cards are flipped face up during each turn.The object of the game is to turn over matching pairs of cards. An online version of this game includes three different sets of cards: one has images of animals on the cards, one has images of babies, and one has images of holiday scenes.Are these three versions equally difficult? To investigate, a teacher randomly assigned her students to three groups and each group played a different version of the game. They recorded the amount of time (in seconds) it took to complete the game.The DCMP One-way ANOVA tool at https:\/\/dcmathpathways.shinyapps.io\/ANOVA\/wasused to create the following partially filled-in ANOVA table.<\/div>\n<\/div>\n
\n\n\n\n\n\n\n
Source<\/td>\nDf<\/td>\nSum sq<\/td>\nMean sq<\/td>\nF value<\/td>\n<\/tr>\n
Group<\/td>\n2<\/td>\n177.4<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Error<\/td>\n27<\/td>\n5715.0<\/td>\n<\/td>\n<\/td>\n<\/tr>\n
Total<\/strong><\/td>\n29<\/strong><\/td>\n5892.4<\/strong><\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
\n
\n
\n

Question 1<\/h3>\n
1) Which of the following is an appropriate description of the variability in this dataset?<\/div>\n
a) The amount of variation between the groups (the differences between the versions)is large relative to the amount of variationwithin the groups (the differences between the individual student performances).<\/div>\n
b) The amount ofvariation between the groups (the differences between the versions)is small relative to the amount of variationwithin the groups (the differences between the individual student performances).<\/div>\n
Hint: Look back at Preview Assignmentand In-Class Activity 14.A to see which sum of squares measures between-groups variabilityand which sum of squares measures within-groups variability.<\/div>\n<\/div>\n<\/div>\n
<\/div>\n
\n
\n

Question 2<\/h3>\n
\n
2) Usethe informationin the ANOVA table to determine if there is evidence that the mean time to complete the game is not the same for all threeversions.<\/div>\n
Hint: You may want to fill out the rest of the ANOVA table to keep your information organized. Look back at Preview Assignment 14.B to see how to conduct a one-way ANOVA F-test.<\/div>\n<\/div>\n
\n
Part A: Calculate the F-statistic. Round your answer to fourdecimal places.<\/div>\n
Part B: Using your answer from Part A and the FDistribution tool(i.e., data analysis tool), calculate the P-valueathttps:\/\/dcmathpathways.shinyapps.io\/FDist\/.Express your answer as a proportion and round to four decimal places.<\/div>\n
Part C:Based on your answer from Part B, which of the following is an appropriate conclusion?<\/div>\n
a) Thesedata provide strong evidence to suggest that the mean timesto completethe gamefor all three versions are equal.<\/div>\n
b) Thesedata provide strong evidence to suggest that the mean timesto completethe gamefor all three versions are different from eachother.<\/div>\n
c) Thesedata provide strong evidence to suggest that a mean time to complete the game for at least one version is different from the others.<\/div>\n
d) Thesedata do not provide sufficient evidence to decide whether themean timesto completethe gameforall three versions are different.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
Questions 3\u20135: Sample data were used to fit a linear regression model that could be used to predict the prices of used cars based on the cars\u2019 mileage.<\/div>\n
\n
\n

Question 3<\/h3>\n
3) The coefficient of determination (\ud835\udc452) for this model was 0.628. Which of the following is an appropriate interpretation of this value?<\/div>\n
a) In this sample, 62.8% of the variation in car prices was explained by the linear regression model using mileage as a predictor.<\/div>\n
b) In this sample, 62.8% of the variation in car prices remained unexplained after using the linear regression model with mileage as a predictor.<\/div>\n
c) In this sample, 62.8% of the car prices were on the regression line. In other words, the model correctly predicted the prices of 62.8% of the cars.<\/div>\n
d)In this sample, 62.8% of the car prices were not on the regression line. In other words, the model incorrectly predicted the prices of 62.8% of the cars.<\/div>\n
Hint: Look back at In-Class Activity 6.Cto review the interpretation of the coefficient of determination.<\/div>\n<\/div>\n<\/div>\n
\n
\n

Question 4<\/h3>\n
4) Which of the following symbols would be used to represent thepredicted price of a car?a)\ud835\udc66b)\ud835\udc66\u0305c)\ud835\udc66\u03025)Which of the following symbols would be used to represent the mean price of all the cars in the dataset?<\/div>\n
a) \ud835\udc66<\/div>\n
b) \ud835\udc66\u0305<\/div>\n
c) \ud835\udc66<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":23592,"menu_order":68,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5528","chapter","type-chapter","status-publish","hentry"],"part":5514,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5528","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5528\/revisions"}],"predecessor-version":[{"id":5636,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5528\/revisions\/5636"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5514"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5528\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5528"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5528"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5528"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5528"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}