You would like to determine if teacher A gives different grades from teacher B in the...

You would like to determine if teacher A gives different grades from teacher B in the same class at a significance level of 0.01. You take a random sample of 85 students from teacher A, 61 of whom passed the class. You also take a random sample of 70 students from teacher B, 56 of whom passed the class.

a) What is the estimate of the difference in proportion of students who pass? Find the estimate of pA − pB.

b) Is it appropriate to assume that the sampling distribution of the difference in proportions is normally distributed?

c) Find a 90% confidence interval for the difference in part (a) and interpret it.

d) Your original goal is to test to see if the two teachers are different. What are the hypotheses for this test?

e) Calculate the z-test statistic for the tests defined in part (d). f) Find the P-value for the test defined in part (d). g) State your conclusion for the hypothesis test, and then interpret the result in the context of the problem.

Solutions

Expert Solution

Let denote the proportions of people who passed the class from teacher A and teacher B respectively.

a) The estimate of the difference in proportion of students who pass is

b) Since and , so it is appropriate to assume that the sampling distribution of the difference in proportions is normally distributed

d) and e)

orchestra answered 11 months ago

Next > < Previous

Related Solutions

3. UTRGV researchers would like to determine if there is a significant difference between the grades...

3. UTRGV researchers would like to determine if there is a significant difference between the grades achieved in the fall versus spring semester. Grades were recorded for a group of 7 students in both semester and are listed below (α = .05). Participant Fall Spring 1 85 89 2 68 84 3 76 79 4 77 82 5 89 90 6 93 91 7 90 90 a. Will we need a one- or two-tailed hypothesis test? b. State your null...

A portfolio gives at 10% return with a standard deviation of 18%. You would like the...

A portfolio gives at 10% return with a standard deviation of 18%. You would like the standard deviation to drop to 14%. What should you do? What should you do if you want the standard deviation to rise to 23%. OUR NOTES give the answers, however, I don't understand how they reached the numbers. The answer to the first part is to add more risk-free assets until they account for 4/18 of the portfolio The answer to the second part...

A task requires the completion of four activities. A teacher would like to know if differences...

A task requires the completion of four activities. A teacher would like to know if differences in the sequence of the four activities results in different task completion times. The teacher selects three students and demonstrates the activities in random order to the students. Then each student completes the task with each of the activity sequences. The completion times are recorded. The following table shows the minutes for each student to complete each task. Time (minutes) Sequence Allen Carla Henry...

......C++ PROGRAM.... Teacher would like us to split this program into a header file(filename.h), and a...

......C++ PROGRAM.... Teacher would like us to split this program into a header file(filename.h), and a .cpp file(filename.cpp). He gave us all the code, we just need to split it up. I do not quite understand how to do it. Please send output screenshot to show validation. #include <iostream> using namespace std; //public class class Account{ public: //instance variables double amount; //creates account and sets amount with users account set-up value Account(double a){ amount = a; } //adds...

Your clints, Jamal and Chyna Gwynn, would like you to determine if they are on track...

Your clints, Jamal and Chyna Gwynn, would like you to determine if they are on track to meet the education funding objective of their son Jarius. Jarius is currently 13 years of age. Jamal and Chyna have high hope for Jarius's future education. Use the following date to determine whether or not Jamal and Chyna need to save more to fund Jarius's educational needs. * Combined federal and state marginal tax bracket: 29 percent * After-tax rate of return before...

You would like to determine if a prospective customer is more likely to purchase a product...

You would like to determine if a prospective customer is more likely to purchase a product after viewing a promotional advertisement for that product. You have the following data from the focus group. Customer Likely to Purchase Likely to Purchase After Promotion A 54 61 B 39 40 C 62 57 D 78 80 E 90 93 F 25 44 G 35 40 Conduct a hypothesis test using a 0.05 level of significance. Remember to show your work and indicate...

You would like to determine who in a group of 100 students carries antibodies for a...

You would like to determine who in a group of 100 students carries antibodies for a certain virus. You can perform blood tests on each student individually, which would require 100 tests. Instead, you can partition the students into 10 groups of 10. Combine the blood samples of the 10 students in each group, and analyze the combined sample. If none of the 10 students in that group carries the antibodies, the test will show negative, while if one or...

select any company that you would like to work for and b) decide the position you...

select any company that you would like to work for and b) decide the position you want to apply for (salesperson, in marketing, trainee, Intern, etc.), then prepare: c) A post interview email.

You determine the format. I would like you to use some computer application, not pen and...

You determine the format. I would like you to use some computer application, not pen and paper. I would suggest WORD for any analysis comments and EXCEL for any spreadsheet analysis (Horizontal/Vertical) You are analyzing a company from a financial standpoint and comparing them to another company. Make it easy for us to read and understand. Make a recommendation to deal with this company or not based on your analysis. Choose a company from the following public companies. That means...

Senario: You are watching a group of children run relay races. You would like to determine...

Senario: You are watching a group of children run relay races. You would like to determine the speed of that the children run. You select 30 children and time them in their relay races. e) What is the parameter for the study? f. What is the statistic for the study? g. Is the study an experiment or an observational study? h. For the study, should you use a proportion or an average?

Subjects