Question

In: Statistics and Probability

A professor has a teaching assistant record the amount of time (in minutes) that a sample...

A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion. The assistant observed 8 students in a class who used a slide show presentation and 8 students in a class who did not use a slide show presentation.

With Microsoft
PowerPoint
Without
Microsoft
PowerPoint
6 4
11 14
10 18
7 21
19 8
9 12
15 13
5 23

Use the normal approximation for the Mann-Whitney U test to analyze the data above. (Round your answer to two decimal places.)
z =

Solutions

Expert Solution

Solutions:-

For the study of the performance of the studies in two different conditions we have to conduct Mann-Whitney U test

The null ad alternative hypothesis are

Ho: f(x) =f(y) The performance of two independent students are equal

Ascending order of the give n data is

Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Data 4 5 6 7 8 9 10 11 12 13 14 15 18 19 21 23

Rank table as shown in the below:

With Microsoft PPT Rank-1 With Microsoft PPT Rank-2
6 3 4 1
11 8 14 11
10 7 18 13
7 4 21 15
19 14 8 5
9 6 12 9
15 12 13 10
5 2 23 23

Total R1 = 56

Total R2 = 87

Now test statistics here n = 8 as 8 rows

u1 = n1n2 + n2(n2+1) / 2 - R1

= 8*8 + (8*9) / 2-56

= 44

u2 = n1n2 + n2(n2 + 1) / 2 - R2

= 8*8 + (8*9) / 2 - 87

= 13

m = E(U) = n1*n2 / 2

= 8*8 / 2 =32

Var(u) = n1n2 + n2(n2+1) / 12

= 90.667

z = u - e(u) / sqrt var(u)

= 13 - 32 / sqrt(90.667)

= - 1.9995

Z ~= -2.00

So here we retain the null hypothesis.

Za/2 = 0.005 = Z0.005/2 = 1.96 from z table

So

Z = -2.00 > 1.96

we accept null hypothesis and retain it.

Please like.


Related Solutions

A professor has a teaching assistant record the amount of time (in minutes) that a sample...
A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion. The assistant observed 8 students in a class who used a slide show presentation and 8 students in a class who did not use a slide show presentation. With Microsoft PowerPoint Without Microsoft PowerPoint 11 19 10 8 18 12 6 9 5 23 4 7 13 14 15 21 Use the normal approximation for the...
A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion.
A professor has a teaching assistant record the amount of time (in minutes) that a sample of 16 students engaged in an active discussion. The assistant observed 8 students in a class who used a slide show presentation and 8 students in a class who did not use a slide show presentation. With MicrosoftPowerPoint WithoutMicrosoftPowerPoint 19 18 6 5 13 10 11 8 23 9 15 21 14 12 7 4 Use the normal approximation for the Mann-Whitney U test...
Professor Trelawney’s research assistant is hard at work again. This time the Professor has asked the...
Professor Trelawney’s research assistant is hard at work again. This time the Professor has asked the assistant to begin some basic inferential analysis. The assistant has been given a data set consisting of 45 observations taken by the professor for a study into neighborhood design and crime. The assistant is now at the point of trying to apply one of the theoretical distributions to the results obtained in the first round of analysis. Should the assistant try to apply the...
The amount of time (in minutes) that a party hat to wait to be seated in...
The amount of time (in minutes) that a party hat to wait to be seated in a restaurant has an exponential distribution with a mean 15. Find the probability that it will take between 10 and 20 minutes to be seated for a table. If a party has already waited 10 minutes for a table, what is the probability it will be at least another 5 minutes before they are seated? If the restaurant decides to give a free drink...
The amount of time, in minutes that a person must wait for a bus is uniformly...
The amount of time, in minutes that a person must wait for a bus is uniformly distributed between 4 and 16.5 minutes, X~U(4, 16.5). a.) Find the mean of this uniform distribution. b.) Find the standard deviation of this uniform distribution. c.) If there are 16 people waiting for the bus and using the central limit theorem, what is the probability that the average of 16 people waiting for the bus is less than 8 minutes? Please type detailed work...
An accounting professor at Middleton University devotes 60 percent of her time to teaching, 30 percent...
An accounting professor at Middleton University devotes 60 percent of her time to teaching, 30 percent of her time to research and writing, and 10 percent of her time to service activities such as committee work and student advising. The professor teaches two semesters per year. During each semester, she teaches one section of an introductory financial accounting course (with a maximum enrollment of 40 students) and one section of a graduate financial accounting course (with a maximum enrollment of...
A statistics professor believes that the amount of time a student spends studying is predictive of...
A statistics professor believes that the amount of time a student spends studying is predictive of their test scores. The professor obtains study time (in hours per week) and test grades from a random sample of 9 students. The data is presented in the table below: Hours Spent Studying Per Week Test Scores 11 80 2 37 1 14 4 66 3 43 5 52 7 96 6 51 3 44 ΣX= ΣX2= ΣY= ΣY2= ΣXY= 1A. Create the regression...
The time to process hot-rolled steel has a standard deviation of 0.9 minutes. A sample of...
The time to process hot-rolled steel has a standard deviation of 0.9 minutes. A sample of size 30 is selected which has an average of 5.5 minutes. (a) Find a 99% confidence interval for the mean time to process hot-rolled steel. (b) Find a 95% confidence interval for the mean time to process hot-rolled steel. (c) Find a 90% confidence interval for the mean time to process hot-rolled steel. (d) What happens to the confidence interval as α significance level...
1. A study of the amount of time it takes a recording artist to record a...
1. A study of the amount of time it takes a recording artist to record a CD shows that the mean is 11.2 hours with a standard deviation of 6.6 hours. If 40 recording artists are randomly selected, find the probability that their mean recording time is between 9.75 and 12.55 hours. Probability Statement:: ________________________ z-Score: ____________ Answer
The dataset in the table shows the ratings for a teaching assistant as a function of...
The dataset in the table shows the ratings for a teaching assistant as a function of both the class that the teaching assistant taught and the GPA of the student providing the ratings. (25 pts + 5 bonus pts) Class 1 Class 2 Class 3 Rating GPA Rating GPA Rating GPA 3.17 1 3.17 1 7.25 3.667 3.75 2.333 6.67 2.667 2.58 2 6.08 3.667 4.92 2.333 3.17 1.667 9 3 6.67 3.333 3.75 2.667 4.92 1.667 3.75 1.333 4.92...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT