GGU – Math 40
Closing Challenge – Spring 2022
Dr. David Fogarty
Scholar Identify: Alex J. Vazquez
Your Rating: ________________________________________________________
THE SCENARIO: You are the Director of Admissions for a large business school. College students looking for admission should take the GMAT (Graduate Administration Admission Take a look at). You wish to collect some inferential statistics about your college students’ GPA’s. You additionally want to decide if a scholar’s GMAT rating is beneficial for predicting the scholar’s GPA at commencement.
THE DATA FILE: The GMAT scores and GPA’s at commencement of 20 randomly chosen college students are contained in the file: GMAT.xlsx, situated in Session eight. For linear regression, the X-variable is the GMAT rating, and the Y-variable is GPA.
INSTRUCTIONS: Reply all the questions beneath. All calculations have to be carried out with Excel or PHStat. Connect Excel or PHStat output the place indicated. You will obtain zero credit score for any reply missing the required Excel or PHStat output.
ROUND OFF ALL CALCULATIONS TO AT LEAST FOUR DECIMAL PLACES. Spotlight the cells with output the place decimal locations want setting. Then use the “Improve Decimal” software on Excel’s Dwelling/Quantity menu. You probably have issues acquiring the required decimal locations, contact me.
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1. Discover the imply and normal deviation of the pattern GPA: [4 POINTS]
PASTE EXCEL DESCRIPTIVE STATISTICS BELOW. [IF YOU FORGOT HOW TO DO THIS, SEE TOPIC 2 CHAPTER 3 EXAMPLES.]
Pattern Imply: ____________
Pattern Customary deviation: _____________
2. Assume that the inhabitants is generally distributed, however the inhabitants normal deviation isn’t identified. Use your pattern knowledge to seek out a 95% confidence interval for the true imply GPA of all college students in the MBA program: [6 POINTS]
PASTE PHSTAT OUTPUT BELOW:
State the margin of error of the confidence interval: ______________
three. Assume that the inhabitants normal deviation is zero.30 and assume the inhabitants is roughly usually distributed. Discover the pattern measurement that might be required to find out a 95% confidence interval for the true imply GPA if we wish to be inside zero.10 of the true imply. That’s, we would like the margin of error, e, to not exceed zero.10. [4 POINTS]
PASTE PHSTAT OUTPUT BELOW:
four. Utilizing your pattern knowledge, take a look at this speculation at the alpha = zero.01 significance stage. You could assume that the inhabitants normal deviation isn’t identified and that the inhabitants is roughly usually distributed. [14 POINTS]
(a) Is there ample proof to conclude that the imply GPA for all college students is greater than three.2?
PASTE PHSTAT OUTPUT BELOW:
(b) Take a look at the speculation once more, altering alpha to zero.05 however not altering the rest.
PASTE PHSTAT OUTPUT BELOW:
Now mark all of the following statements about the two speculation checks both T(TRUE) or F(FALSE).
_________ The p-value is the chance that the null speculation will probably be rejected.
_________ The second take a look at has a smaller “reject” area than the first.
_________ The take a look at statistic measures the distance between the imply being examined and the pattern imply.
_________ The null speculation will probably be rejected supplied alpha exceeds the p-value.
_________ The crucial worth is the boundary between the “reject” area and the “don’t reject” area.
_________ The p-value is the chance of getting a take a look at statistic equal to, or extra excessive than the pattern outcome, if the null speculation is true.
5. Suppose it’s identified that eight out of the 20 college students in the pattern are girls. [8 POINTS]
(a) Discover a 95% confidence interval for the true proportion of all MBA college students who are girls.
PASTE PHSTAT OUTPUT BELOW:
(b) What’s your opinion of the precision of this confidence interval? Give a motive for your reply.
6. Assume that the inhabitants proportion is zero.45, and discover the pattern measurement that might be required to find out a 95% confidence interval if we wish to be inside zero.05 of the true proportion of girls MBA college students. That’s, we would like the margin of error, e, to not exceed zero.05. [4 POINTS]
PASTE PHSTAT OUTPUT BELOW:
LINEAR REGRESSION – Use the pattern to finish this part. Keep in mind, the X variable is GMAT SCORE, and the Y variable is GPA
7. PASTE A SCATTER PLOT BELOW: [4 POINTS]
eight. Carry out the regression Assessment utilizing PHSTAT and PASTE THE PRINTOUT BELOW: [4 POINTS]
NOTE: BEFORE YOU COPY THE PRINTOUT, CHANGE THE FORMAT OF THE P-VALUE FOR GMAT TO SCIENTIFIC NOTATION. HIGHLIGHT THE CELL, THEN ON THE EXCEL HOME/NUMBER MENU, SELECT “SCIENTIFIC” FROM THE DOP-DOWN BOX.
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9. The regression output. [10 POINTS]
i. The regression equation is: ____________________________________
ii. The slope of the equation is: ___________________________________
iii. The y-intercept of the equation is: ________________________________
iv. The usual error of the estimate is: ____________________________
v. The coefficient of willpower is: _____________________________
10. Utilizing the Excel printout from Question Assignment eight, take a look at the speculation that there is no such thing as a linear relationship between X and Y. Take a look at at alpha = zero.05 significance stage. [8 POINTS]
i. State the null speculation: _______________________
ii. State the alternate speculation: ___________________
iii. p-value: __________________________________
iv. Take a look at outcome and motive for take a look at outcome: ________________________________
11. Interpretation. [6 POINTS]
(a) What does the y-intercept of this regression equation signify?
(b) State the actual that means of the slope on this regression equation.
(c) Predict the GPA of a scholar with a GMAT rating of 600. _______________
12. [12 POINTS] (a) PASTE RESIDUAL PLOT BELOW:
(b) From the residual plot, do you suppose that the two regression assumptions listed beneath are happy? Give the motive for your conclusion.
Linearity: ___________________________________
Motive: ____________________________________
Equal Variance: ______________________________
Motive: ____________________________________
13. [8.POINTS]
(a) PASTE A NORMAL PROBABILITY PLOT OF RESIDUALS BELOW:
(b) From the regular chance plot, do you suppose the normality assumption for regression is happy? Give the motive for your conclusion.
14. Decide 95% confidence and prediction intervals for X = 600. [4 POINTS]
PASTE PHSTAT OUTPUT BELOW:
15. Talk about this mannequin. How good do you suppose the mannequin is for predicting GPA? Give causes for your reply. Then state at the least two different doable impartial variables that you just suppose could be helpful for predicting GPA. [4 POINTS]
This last undertaking is due on session 15, April 22, 2021. You want submit this Microsoft Phrase File on this given format. Additional, you’ll be able to both submit this work on-line or in-class. The undertaking is value 26% of your total course grade and it’ll not be returned.
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MATH 40 – C1 Web page 1
