BUSI 410 FINAL EXAM Fall 2021 This exam consists of three short cases Case Midterm Grades TJ Maxx Bike Sharing Pages Points 2 4 5 8 9 13 Total 35 30 35 100 Answer the questions after each case Show all of your work on the exam paper The cases questions are not ordered in difficulty If you are stuck try the next question This exam is open book note and laptop However no communication of any kind is allowed verbal written or electronic Disable your laptop s Wi Fi Internet connectivity Turn off and put away your cell phone Name Please Print Section please circle Honor Code Pledge I will neither give nor receive unauthorized aid during this exam Signature 12 30 11 00 9 30 2 00 DO NOT TURN TO THE NEXT PAGE UNTIL YOU ARE ASKED TO Page 1 of 13 Midterm Grades The midterm grades for a random sample of 83 students have been collected to study the students performance in this exam The midterm exam had 60 points in total with 30 points assigned to each of the two questions in the exam The following snapshot shows the grades of each student for each of the two questions in the midterm exams with the summary statistics presented at the bottom 1 We are interested in finding out whether the average performance of students on these two questions are different Please formally state the null and alternative hypothesis of the test 2 pts Ha 1 2 H0 1 2 2 Indicate a function in Excel that you would use to perform the statistical test in question 1 use the 5 significance level for the test Be sure to indicate how you would use the output of your function to make your conclusion 3 pts p value T TEST B2 B84 C2 C84 2 1 if p value 5 we reject the null and accept the alternative hypothesis otherwise we conclude that we cannot reject the null hypothesis Page 2 of 13 3 The p value of the test above can also be calculated using either the T DIST RT or T DIST 2T function in Excel depending on your hypothesis test in question 1 Please specify the numbers that must be put into this Excel function by showing all your calculation steps 6 pts SE s sqrt N 4 31 sqrt 83 0 47 t stat Sample Mean Difference SE 1 42 0 47 2 99 DF N 1 83 1 82 p value T DIST 2T t stat DF T DIST 2T 2 99 82 0 004 4 Construct an approximate 95 confidence interval for the mean difference between the scores of questions 1 and 2 4 pts Approximate 95 MoE 2 SE 2 0 47 0 94 Approximate 95 CI Sample Mean Differnce MoE 1 42 0 94 2 36 0 48 5 In the collected sample the scores of 36 students in the second question are at least as good as those in the first question Construct a conservative approximate 95 confidence interval for the percentage of students who are expected to do in the second question at least as good as in the first question 4 pts Sample Proportion 1 sqrt N 36 83 1 sqrt 83 32 54 Page 3 of 13 6 We would like to test and see whether the average total grade i e sum of scores for the two questions is greater than 50 The standard deviation of the total grade across the sampled students is 6 78 Please formally state the null and alternative hypothesis of the test perform the test at the 5 significance level and state your conclusion in practical terms 6 pts Ha total 50 H0 total 50 Sample mean of total grade sample mean of Q1 score sample mean of Q2 score 50 74 SE s sqrt N 6 78 sqrt 83 0 74 t stat sample mean 50 SE 50 74 50 0 74 0 996 p value T DIST RT t stat DF T DIST RT 0 996 82 0 16 p value 5 so we cannot reject the null hypothesis in other words we cannot reject the fact that the average total grade could be smaller than 50 7 Construct an exact 90 confidence interval for the mean total score 4 pts MoE SE critical t 0 74 T INV 2T 0 1 82 1 24 90 CI Sample mean of total grade MoE 50 74 1 24 49 50 51 98 8 A second sample of 83 students have been randomly selected whose total grade has an average of 53 24 and standard deviation of 8 41 Construct an approximate 95 confidence interval for the mean difference between the scores of these two sets of students 6 pts Pooled SE 1 19 MoE 2 SE 2 1 19 2 38 CI 53 24 50 74 2 38 0 12 4 88 Page 4 of 13 Predicting TJ Maxx Sales TJ Maxx a discount retailer would like to compare the sales per square foot in its different locations taking into account the substantial differences in income and population The management is planning to use this information to guide their location selections for new store openings To perform this analysis TJ Maxx gathered retail sales data at 87 locations For each of the locations in the dataset we have values of the following variables Variable STORE ID SALES INCOME POPULATION MARKET Coding explanation Each store has a unique identifier number Sales per square foot in dollars sq ft The median household income in the surrounding community in dollars The size of the surrounding population in thousands The market type which can take 3 possible values Rural Urban and Suburban In order to complete the analysis TJ Maxx used the Market variable to create two indicator variables Urban which takes on the value 1 if the store is in an urban market and 0 otherwise and Rural which takes on the value 1 if the stores is in a rural market and 0 otherwise A representative sample of the data from these stores is presented below Page 5 of 13 Please use the results of running this regression presented below to answer the subsequent questions SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0 8314 0 6913 0 6762 64 4651 87 ANOVA Regression Residual Total df 4 86 SS MS F 762953 4298 190738 36 45 89752 340771 0191 4155 7441 1103724 449 Significance F 3 47666E 20 Intercept Income Population 000 Urban Rural Coefficients Standard Error 85 6169 0 0009 0 0412 21 0183 27 2628 143 524 0 00475 0 234 199 001 65 414 t Stat 1 6764 5 1818 5 6906 9 4680 2 3994 P value 0 0975 0 0000 0 0000 0 0000 0 0187 Lower 95 Upper 95 26 7952 0 0066 0 3164 240 8130 119 6481 313 8435 0 0029 0 1525 157 1888 11 1794 1 One of the cells from the regression output is covered in grey What number should appear in this cell 2 pts 82 87 4 1 2 Interpret …