Final Scores

Two different forms of the Final (A and B) were given to students in two sections of an U of I course in Spring 2015. The scores are as follows.

scores <- c(74, 66, 52, 82, 66, 51, 67, 73, 53, 64, 73, 61, 71, 67, 64, 83, 61, 65, 81, 65, 80, 66, 74, 76, 47, 71, 73, 74, 81, 41, 56, 41, 74, 71, 40, 53, 85, 70, 74, 60, 44, 51, 68, 46, 65, 80, 72, 24, 60, 77, 74, 72, 71, 57, 73, 77, 42, 66, 58, 30, 38, 45, 65, 45, 75, 54, 45, 77, 72, 73, 68, 77, 50, 55, 71, 57, 75, 47, 83, 78, 71, 58, 55, 73, 80, 60, 65, 80, 61, 63, 50, 64, 66, 69, 65, 77, 84, 71, 70, 82, 74, 65, 78, 72, 70, 52, 72, 76, 62, 54, 67, 72, 75, 75, 54, 79, 63, 60, 80, 63, 68, 75, 50, 71, 83, 78, 63, 63, 81, 71, 56, 72, 71, 59, 79, 61, 73, 70, 64, 78, 71, 80, 42, 68, 38, 72, 82, 66, 74, 71, 80, 79, 42, 81, 68, 70, 61, 27, 78, 56, 79, 62, 70, 62, 75, 70, 41, 74, 53, 45, 73, 83, 63, 69, 51, 59, 38, 58, 63, 51, 71, 67, 58, 52, 60, 75, 75, 40, 65, 48, 56, 58, 60, 58, 50, 53, 83, 46, 75, 23, 49, 57, 52, 57, 67, 50, 77, 78, 32, 74, 77, 79, 62, 62, 72, 69, 63, 57, 60, 77, 68, 53, 67, 65, 48, 61, 32, 74, 48, 73, 71, 49, 77, 74, 69, 67, 52, 76, 37, 66, 71, 71, 82, 75, 65, 53)

Form <- as.factor(c("A", "A", "A", "B", "A", "A", "A", "A", "A", "A", "A", "A", "A", "B", "A", "A", "A", "B", "A", "A", "A", "A", "A", "A", "B", "A", "A", "A", "A", "A", "A", "A", "A", "B", "A", "B", "A", "A", "A", "B", "A", "A", "B", "A", "B", "A", "A", "B", "B", "B", "A", "B", "A", "A", "A", "A", "B", "A", "B", "B", "B", "B", "A", "A", "A", "A", "A", "A", "B", "A", "B", "B", "A", "B", "B", "A", "A", "A", "B", "B", "B", "A", "B", "B", "A", "B", "A", "A", "A", "A", "A", "B", "A", "A", "B", "A", "A", "B", "B", "A", "A", "B", "A", "A", "A", "B", "A", "B", "A", "B", "A", "A", "A", "B", "A", "A", "B", "B", "A", "B", "A", "A", "A", "B", "A", "B", "B", "A", "A", "B", "A", "B", "B", "A", "A", "B", "A", "A", "A", "B", "A", "B", "B", "A", "B", "A", "B", "B", "A", "A", "A", "B", "B", "B", "A", "B", "A", "B", "A", "A", "A", "A", "B", "B", "A", "B", "A", "A", "B", "A", "A", "A", "B", "B", "A", "A", "A", "B", "B", "A", "B", "B", "A", "A", "B", "B", "B", "A", "A", "A", "A", "A", "B", "A", "B", "B", "A", "B", "B", "A", "B", "A", "B", "B", "B", "B", "A", "B", "A", "A", "A", "A", "A", "B", "B", "A", "B", "B", "A", "A", "A", "A", "B", "B", "B", "A", "A", "A", "B", "A", "A", "A", "A", "A", "B", "B", "B", "A", "B", "A", "A", "A", "A", "B", "B", "B"))

Name <- c("Presley", "Jeryl", "Thurston", "Selmer", "Earle", "Jovanni", "Kirt", "Irvin", "Green", "Mallory", "Acie", "Ellery", "William", "Edson", "Elizebeth", "Ariel", "Grafton", "Betsy", "Maverick", "Cain", "Lorraine", "Davy", "Warner", "Trayvon", "Trae", "Golda", "Evita", "Bryana", "Maybelle", "Evaline", "Dema", "Garnet", "Arleen", "Treva", "Margretta", "Augusta", "Margret", "Deborrah", "Mathews", "Brittnay", "Leonard", "Glinda", "Mel", "Merlene", "Audrey", "Alonso", "Merry", "Cordella", "Eustace", "Violeta", "Olar", "Beecher", "Bambi", "Pamelia", "Bernice", "Magdalena", "Aileen", "Rosann", "Josiephine", "Otha", "Sherryl", "Bobbie", "Bettye", "Alina", "Kathy", "Wendy", "Kelsey", "Ali", "Romie", "Breanna", "Kenia", "Tammi", "Esley", "Michal", "Jerimy", "Hezekiah", "Carrol", "Victoriano", "Mckayla", "Verlyn", "Hattie", "Oda", "Uriel", "Tonya", "Tarah", "Wilmer", "Hjalmer", "Kellan", "Danita", "Gino", "Mya", "Kennedy", "Steven", "Kymani", "Kaylynn", "Adelyn", "Addisyn", "Alcee", "Edith", "Nia", "Dove", "Fran", "Shreya", "Lola", "Fredericka", "Melvina", "Tracey", "Jackeline", "Burrell", "Isam", "Elwood", "Canyon", "Anita", "Javen", "Randel", "Evan", "Dori", "Lula", "Gwyneth", "Lucian", "Alycia", "Noma", "Lutie", "Geraldine", "Mechelle", "Venita", "Hamilton", "Richelle", "Deirdre", "Gladyce", "Birdie", "June", "Eleanora", "Sage", "Josephine", "Lemmie", "Jedidiah", "Kamilah", "Darryn", "Ivor", "Jiles", "Essence", "Shaniqua", "Leyla", "Aurthur", "Jaxon", "Renea", "Quintin", "Mohamed", "Diandra", "Dara", "Konner", "Waneta", "Alan", "Ione", "Tammie", "Missy", "Miah", "Ashely", "Bennett", "Cristopher", "Evelyn", "Romello", "Mahalie", "Daunte", "Marcello", "Brandy", "Doc", "Van", "Refugio", "Tab", "Eli", "Atticus", "Lemon", "Lone", "Chas", "Senora", "Davian", "Rexford", "Xena", "Kianna", "Garvin", "Maeve", "Willodean", "Kaylie", "Caitlin", "Kelvin", "Albina", "Araminta", "Add", "Quiana", "Alcie", "Paityn", "Anice", "Yazmin", "Ancil", "Newt", "Gustave", "Briana", "Malorie", "Alston", "Chynna", "Micky", "Merrilee", "Harper", "Arnie", "Griselda", "Hadassah", "Brain", "Vita", "Pearlie", "Leandra", "Braulio", "Watson", "Kelis", "Markita", "Stella", "Kelli", "Amiah", "Asberry", "Jeramie", "Doll", "Trish", "Zora", "Keira", "Kaeden", "Erving", "Myrna", "Theo", "Sie", "Cathie", "Latoya", "Norma", "Harmony", "Freddy", "Vinton", "Sarahi", "Jacki", "Lonie", "Casper", "Bose", "Chyna", "Oswaldo", "Judith", "Ari", "Kiefer")

Students' names and scores have been altered to protect privacy. Names were randomly chosen from the file baby-names.csv. Copy and paste the data to your R console.

a. Calculate the mean and population standard deviation of the scores in each form. Enter your answers to 2 decimal places. If you use the sd() function, don't forget to use the factor √(n-1)/n to convert the sample sd to population sd. Note that this is one of the rare occasions that we have data for the whole population (all students in the class).

Form A:    mean =    population standard deviation =

Form B:    mean =    population standard deviation =

b. Perform a two-sample t-test to determine if the difference in the means between the two forms is significant at the 5% level. Don't forget to set var.equal=TRUE. Enter the (two-sided) p-value to 3 decimal places.

P-value of the t-test =

Is the difference in means between the two forms significant at α = 5%?
yes
no

c. Use the wilcox.test() function to perform the Wilcoxon Mann-Whitney rank sum test to determine if there is significiant difference in the difficulty between the two exam forms for any segment of the population. Enter the p-value to 3 decimal places.

P-value of the Wilcoxon test =

Is there a significant difference in the difficulty between the two exam forms at α = 5%?
yes
no

d. After preparing the two forms of the final, the instructor of the course sensed that Form B might be harder. After getting the scores, he was convinced that his hypothesis was true even though he didn't do any hypothesis testing because he didn't know statistics. (We know that his conclusion was correct because the hypothesis tests should be one-sided and the p-values are half of those computed above. In this case, both the t-test and Wilcoxon Mann-Whitney test give the same conclusion.) Noticing that the two means differ by about 3 points, the instructor adjusted the scores by adding 3 points to the scores in Form B, but keeping the scores in Form A unchanged. The instructor thought that there should be no significant difference in the difficulty between the two exam forms after the adjustment.

Perform the t-test and Wilcoxon Mann-Whitney test for the adjusted scores. Enter the (two-sided) p-values to 3 decimal places.

P-value of the t-test =

P-value of the Wilcoxon Mann-Whitney test =

Is the difficulty between the two exam forms after adjusting the scores significantly different?
yes
no

e. Kelvin was a student in this class. He asked the instructor to write a recommendation letter to support his application to transfer to another university. The instructor didn't remember this student. He wanted to find out the rank of this student's adjusted Final score in this class. Note that the rank the instructor wanted was in the reverse order provided by the rank() function: the highest score is ranked 1. So you'll have to use rank(-adjusted_scores) instead of rank(adjusted_scores). For simplicity, treat ties in the same way as in the default setting of the rank() function. Calculate the rank of Kelvin's adjusted Final score.