Download Statistical Analysis of Student Performance in EE 300 Exam 3 - Prof. Jon R. Marstrander and more Exams Electrical and Electronics Engineering in PDF only on Docsity!
EE 300, Fall 2006, Exam 3 16 November 2006 Page 1 / 9 Name: Solution_Key
Rules: You may use calculators, pens and pencils, and the text book and your brain. You may unt Show All Work. il both of you have handed NOT work with anyone else on this exam. Do not discuss this test with anyone Attach extra paper if needed. Clearly label all work done outside of-in your papers. This is a test of what you know. the indicated areas. Clearly indicate your final answers. The test is due at the end of the c Good Luck! lass, at 12:15pm. After you have finished the exam, please answer the following questions. They will NOT What grade do you think you made on this exam: ________ affect your grade. How difficult is this exam? (10 = way too hard, 0 = way too Comments: easy): ________
EE 300, Fall 2006, Exam 3, 16 Noveber 2006, Page 2 / 9 Name: Solution_Key Thousands of students have taken a standardized test. You have been hired to perform a statistical analysis of student performance on this test. Since your budget is very limited, you have a single sample of data from the students, given below. This is your data set for all of the statistical analysis you will perform on this test. Test Scores 663 Hours Studied 11 (^629596642689658624 ) (^643706 )
EE 300, Fall 2006, Exam 3, 16 Noveber 2006, Page 4 / 9 Name: Solution_Key entire population, to a 99% confidence level, based on the sample data. 2. [10 points] Compute a confidence interval for the mean of the test scores for the For this one, you should use "Table 2" because you are not given Step 1: Confidence level = 0.99 Step 2: Find c F(c)=1/2(1+0.99) σ. Step 3: Take sample average and sample variance from problem 1.^ F(c)=0.995^ Use T distribution, with (9^ c = 3.36 -1)=8 degrees of freedom !^ Step 4: Compute k^ s^ x^ ==^ 33.608^650 !
k = = (^) =37.64(33.608)( sc n 9 3.36) Answer: !
CONF CONF CONF " " " === 0.990.990.99 { { {((612.35 650 x # k #) 37.64 $$ μ μ $$ (^) ) (687.64 x $ + μ k $) }(} 650 # 37.64)}
EE 300, Fall 2006, Exam 3, 16 Noveber 2006, Page 5 / 9 Name: Solution_Key for the entire population, to a 99% confidence level 3. [10 points] Compute a confidence interval for the standard deviation of the test scores, based on the sample data. For this one, you should use "Table 3." Step 1: Confidence level = 0.99 Step 2: Find c F(c 1 )=1/2(1 1 and c-0.99) (^2) F(c 2 )=1/2(1+0.99) Step 3: Compute (n^ F(c^ Use chi^ c^1 = 1.34^1 )=0.005-squared distribution, with (9^ -^ 1)s^2 , using data from problem 1.F(cc^2 = 21.96^2 )=0.995-1)=8 degrees of freedom Step 4: Compute k^ (n k k k 111 - = (n= 9036/1.34= 6743.271)s^2 - = 90361)s (^21) /c and k 1 2 kkk 222 = (n= 9036/21.96= 411.4745-1)s (^2) /c 2 Answer: !
CONF CONF CONF " " " === 0.990.990.99 { { { k (^) 411.47 (^) 20.29 2 # $ #^2 ## $ (^) $ k # 1 2 } 82.12# 6743.27} }
EE 300, Fall 2006, Exam 3, 16 Noveber 2006, Page 6b / 9 Name: Solution_Key (Problem 4, continued) So... Our sample is +4.46 standard deviations away from the mean of the Null Hypothesis. If we were beneath +2.90 standard deviations away from the mean of the Null Hypothesis, we could attribute that to sampling variation, to within a 99% certainty. However, we are far greater than that threshold, so we Hypothesis, and average this year. support the Alternate Hypothesis, that scores are better than reject the Null
Double Bonus #2: than normal? This bonus question asks you to find what would be called the "p set, for a hypothesis test. In other words, what is the biggest confidence level could you use for your hypothesis test, and pass. On Problem #4, to what degree of confidence is this score higher-level" of a data
In this case, since we are looking for a bigger score, our answer is simply the value of F(t), for the T Using the T F(4.46)=0.9989,-distribution, with (9-score of our sampl-1) = 8 degrees of freedom,e data set. so this data has a p average. -level of 0.9989, or 99.89% confidence of being higher than
EE 300, Fall 2006, Exam 3, 16 Noveber 2006, Page 7 / 9 Name: Sol preparing for the test, and their test scores. (Show all of your intermediate steps!) Did 5. [20 points] What is the correlation between the amount of time that students spentution_Key preparation time significantly help the students' scores? Jus sx = 33.64, from problem 1t run the numbers...
= s^ y^ 10 =^ "^ #^ $^19 %^ &^ '^ (^11 +^7 +^ ...+^12 )
= = y " # $^23 18 =% & '^ "^ #^ $(24^9 1 ()^1 %^ &^ '^ [(^11 (^10 )^2 +^ (^7 (^10 )^2 +^ ...+^ (^12 (^10 )^2 ] s = = y (^) 1.732= 3 sy^2
! So...^ =^ sxy^ 35.63^ =^ #^ $^ %^9 1 "^1 &^ '^ (^ [(^663 "^650 )^ (^11 "^10 )^ +^ (^629 "^650 )^ (^7 "^10 )^ +^ ...+^ (^706 "^650 )^ (^12 "^10 )] !^ This is a positive correlation, and fairly far from zero, so^ time spend studying helped the stude correlation is significant. Let's look at the bonus problems to be sure...^ r^ =^^ ssxxy^ sy^ =^ (33.64(35.63)(1.732) )^ =^ 0.612 nts scores. Intuition seems to say that this^ Yes, it does appear that
EE 300, Fall 2006, Exam 3, 16 Noveber 2006, Page 9 / 9 Name: Solution_Key an 6a. [10 points] Give a simple explanation of what point estimates, confidence intervals,d hypothesis tests are. How are they different? What types of answers do they provide? Statistical Measure Point estimates ProvidesA single number MeaningA best single value for the measured quantity, based on the given sample Confidence intervals Hypothesis tests AA yes/no answer range of numbers A range in which the measured quantity could fall, to a certain confidence levelIs this sample significantly different from the normal errors for a Hypothesis Test.^ 6b. [5 points] Give a simple explanation of the differenc^ case?e between Type I and Type II Type I Error: Rejecting the Null Hypothesis when it is really true. Probability of α Innocent person, when the pr Type II Error: Accepting the Null Hypothesis, when it is really false. Probability of, selected when setting up the test. e.g.: a court decision of Guilty for a truly β, which results from test conditions. e.g.: a court decision of Innocent for aesumption is Innocent. value is significant.^ 6c. [5^ points] Give a simple explanation of what correlation is, and when a correlation^ truly Guilty person, when the presumption is Innocent. Correlation is a number between quantities are related. • • a correlation close to +1 indicates that th decrease together,a correlation close to 0 indicates that there is no relationship between the quantities, and - 1 and +1, which indicates the degree to which twoe two quantities increase or A correlat^ •^ a correlation close to^ other quantity decreases.ion is more significant when it is farther from zero.^ - 1 indicates that one quantity tends to increase as the
