Question

In: Math

A professor has a class with four recitation sections. Each section has 16 students (rare, but...

A professor has a class with four recitation sections. Each section has 16 students (rare, but there are exactly the same number in each class...how convenient for our purposes, yes?). At first glance, the professor has no reason to assume that these exam scores from the first test would not be independent and normally distributed with equal variance. However, the question is whether or not the section choice (different TAs and different days of the week) has any relationship with how students performed on the test.

Group-1	Group-2	Group-3	Group-4
73.5	76.7	75	65.7
81	66.4	77.8	50.5
61.8	60.3	66.7	83
69.5	81	70.3	81.4
77.4	57.9	77.7	74.9
91.2	59.2	68.1	82.9
70.6	67.9	83.5	85.4
64	54.9	87.8	63.6
73.2	63.2	80.6	67.6
77.7	69.8	58.9	73.6
73.6	69.1	86.7	81.5
77.2	51.8	74.7	80.5
54	60.5	66.9	71.8
65.4	55.4	76.7	68.1
77.8	68.2	76.3	55.8
81.6	64.8	69.5	70.4

First, run an ANOVA with this data and fill in the summary table. (Report P-values accurate to 4 decimal places and all other values accurate to 3 decimal places.

Source	SS	df	MS	F-ratio	P-value
Between
Within

To follow-up, the professor decides to use the Tukey-Kramer method to test all possible pairwise contrasts.

What is the Q critical value for the Tukey-Kramer critical range (alpha=0.01)?
Use the website link in your notes (http://davidmlane.com/hyperstat/sr_table.html) to locate the Q critical value to 4 decimal places.
Q =

Using the critical value above, compute the critical range and then determine which pairwise comparisons are statistically significant?

group 1 vs. group 2
group 1 vs. group 3
group 1 vs. group 4
group 2 vs. group 3
group 2 vs. group 4
group 3 vs. group 4
none of the groups are statistically significantly different

Solutions

Expert Solution

	Group-1	Group-2	Group-3	Group-4	Total
Sum	1169.5	1027.1	1197.2	1156.7	4550.5
Count	16	16	16	16	64
Mean, sum/n	73.09375	64.19375	74.825	72.29375
Sum of square, Ʃ(xᵢ-x̅)²	1195.049	941.0294	917.31	1551.929

Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3 = µ4

H1: At least one mean is different

Number of treatment, k = 4

Total sample Size, N = 64

df(between) = k-1 =3

df(within) = k(n-1) =60

df(total) = N-1 =63

SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 + (Sum4)²/n4 - (Grand Sum)²/ N =1071.552

SS(within) = SS1 + SS2 + SS3 + SS4 =4605.318

SS(total) = SS(between) + SS(within) =5676.870

MS(between) = SS(between)/df(between) =357.184

MS(within) = SS(within)/df(within) =76.755

F = MS(between)/MS(within) =4.654

p-value = F.DIST.RT(4.6535, 3, 60) = 0.0054

Decision:

Reject the null hypothesis.

ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	1071.552	3	357.184	4.654	0.0054
Within Groups	4605.318	60	76.755
Total	5676.870	63

At α = 0.01, k = 4, N-K = 60, Q value = 4.5942

Critical Range, CV = Q*√(MSW/n) = 4.5942*√(76.7553/16) = 10.0625

Comparison	Absolute Diff. = (xi - xj)	Critical Range	Results
x̅1-x̅2	8.9	10.0625	Means are not different
x̅1-x̅3	-1.73125	10.0625	Means are not different
x̅1-x̅4	0.8	10.0625	Means are not different
x̅2-x̅3	-10.6313	10.0625	Means are different
x̅2-x̅4	-8.1	10.0625	Means are not different
x̅3-x̅4	2.53125	10.0625	Means are not different

milcah answered 4 months ago

Next > < Previous

Related Solutions

In a large class of introductory Statistics students, the professor has each person toss a coin...

In a large class of introductory Statistics students, the professor has each person toss a coin 29 times and calculate the proportion of his or her tosses that were heads. Complete parts a through d below. The Independence Assumption (is or is not) )_____satisfied because the sample proportions (are or are not)_____independent of each other since one sample proportion (can affect or does not affect)______another sample proportion. TheSuccess/Failure Condition is not satisfied because np=____ and nq=____which are both (less than...

A professor who teaches a large introductory statistics class (197 students) with eight discussion sections would...

A professor who teaches a large introductory statistics class (197 students) with eight discussion sections would like to test if student performance differs by discussion section, where each discussion section has a different teaching assistant. The summary table below shows the average score for each discussion section as well as the standard deviation of scores and the number of students in each section. Sec 1 Sec 2 Sec 3 Sec 4 Sec 5 Sec 6 Sec 7 Sec 8 ni...

COIN TOSSES In a large class of introductory Statistics students, the professor has each student toss...

COIN TOSSES In a large class of introductory Statistics students, the professor has each student toss a coin 16 times and calculate the proportion of his or her tosses that were heads. The students then report their results, and the professor plots a histogram of these several proportions. What shape would you expect this histogram to be? Why? Where do you expect the histogram to be centred? How much variability would you expect among these proportions? Explain why a Normal...

Professor realizes that he hates his class and has decided to give each of his students...

Professor realizes that he hates his class and has decided to give each of his students a 20-point decrease in all their grades for no reason. Help him write the C++ code that will allow him to do this. Consider the code on the next page. It creates an array of 10 structs called students which contains their name and their grade. It is nearly complete. Your task is the following: Complete the user-defined function called subtractTwenty. You will need...

In a section of an English 201 class, the professor decides to be “generous” with the...

In a section of an English 201 class, the professor decides to be “generous” with the students and will grade the next exam in a unique way. Grades will be assigned according to the following rule: The top 10% receive A’s, the next 20% receive B’s, the middle 40% receive C’s, the next 20% receive D’s, and the bottom 10% receive F’s. Some may refer to this type of grading as “curving” which gave rise to the phrase, “Professor, do...

An MPH professor claims that 50 % of the students in his class has a median...

An MPH professor claims that 50 % of the students in his class has a median weight different from 140 lb. He collects the weight of a random sample of 22 students. Enter the following data in SPSS and perform a binomial test using the standard method. Alpha level = 0.05 (Make sure to save your data before start analyzing the data). 135 119 106 135 180 108 128 160 143 175 170 205 195 185 182 150 175 190...

a professor has learned that six students in her class of 19 will cheat on the...

a professor has learned that six students in her class of 19 will cheat on the exam. She decides to focus her attention on eight randomly chosen students during the exam. A. what is the probability that she finds at least one the students cheating? B. what is the probability that she finds at least one of the students cheating if she focuses on nine randomly chosen students?

A professor has learned that eight students in her class of 31 will cheat on the...

A professor has learned that eight students in her class of 31 will cheat on the exam. She decides to focus her attention on ten randomly chosen students during the exam. a. What is the probability that she finds at least one of the students cheating? (Round your final answers to 4 decimal places.) b. What is the probability that she finds at least one of the students cheating if she focuses on eleven randomly chosen students? (Round your final...

A statistics professor has stated that 90% of his students pass the class. To check this...

A statistics professor has stated that 90% of his students pass the class. To check this claim, a random sample of 150 students indicated that 129 passed the class. If the professor's claim is correct, what is the probability that 129 or fewer will pass the class this semester? A) 0.0516 B) 0.9484 C) 0.5516 D) 0.4484 please show work

A Discrete Mathematics professor has a class of students. Frustrated with their lack of discipline, he...

A Discrete Mathematics professor has a class of students. Frustrated with their lack of discipline, he decides to cancel class if fewer than some number of students are present when class starts. Arrival times go from on time (arrivalTime < 0) to arrival late (arrivalTime > 0).Given the arrival time of each student and a threshhold number of attendees, determine if the class is canceled. Input Format The first line of input contains t, the number of test cases. Each...

Subjects