Fall 2016 STA 2023 Fall 2016 PROJECT IMPORTANT NOTE POINTS: nu ru Instructor: Venkateswara Rao Mudunuru YOU MUST SUBMIT THE ANSWERS ONLINE IN THE LINK GIVEN ON CANVAS ANNOUNCEMENTS. LINK WILL BE ACTIVE FROM FRIDAY NOVEMBER 11, 2016 STARTING 8 AM. YOU CAN SUBMIT YOUR RESPONSES ONLY ONCE. ud u THIS IS NOT A TEAM PROJECT. YOU SHOULD DO IT INDEPENDENTLY. PROJECT COVERS QUESTIONS FROM CHAPTERS 4, 6 & 7 OF OUR COURSE MATERIAL. YOU CAN REFER TO SLIDES FOR HELP. PROJECT SCORE WILL BE CONSIDERED AS 0 FOR MULTIPLE SUBMISSIONS (IF ANY). tM MAKE SURE YOU CORRECTLY WRITE YOUR SECTION NUMBER. WRONG SECTION NUMBER SUBMISSIONS WILL NOT BE GRADED. PAPER SUBMISSIONS WILL NOT BE GRADED. BE READY WITH YOUR ANSWERS TO THESE QUESTIONS GIVEN BELOW BEFORE GOING ONLINE FOR SUBMISSIONS. ka THIS PROJECT IS NOT TIMED. HOWEVER, THERE IS NO CHANCE FOR SAVING YOUR ANSWERS AND CONTINUE THEM ON LATER TIME OR DAY. en MAKE SURE YOU HAVE YOUR LAPTOP CHARGED, AND WITH GOOD INTERNET SERVICE. PROJECT SUBMISSION DELAYS WITH ANY REASONS OR SUCH EXCUSES ARE NOT ENTERTAINED. READ THE QUESTIONS THOUGUHLY AND THEN ATTEMPT TO SOLVE THEM. V YOU WILL NEED YOUR EXAM-1 SCORE OUT OF 120 FOR DOING SOME PORTION OF THIS PROJECT. YOUR TEACHING ASSISTANTS CAN NOT HELP YOU IF YOU HAVE ANY CONCERNS ABOUT PROJECT. ALL QUESTIONS AND QUERIES ABOUT THIS PROJECT SHOULD BE ASKED IN PERSON DURING OUR LECTURE OR IN MY OFFICE HOURS OR BY EMAILING TO ME AT VMUDUNUR@MAIL.USF.EDU ON OR BEFORE NOVEMBER 22, 2016 11:59 PM. NO QUESTIONS OR CONCERNS WILL BE ANSWERED AFTER THIS DAY. Venkateswara Rao Mudunuru Fall 2016 P a g e |1 Fall 2016 STA 2023 Fall 2016 PROJECT Instructor: Venkateswara Rao Mudunuru FALL 2016 STA 2023 PROJECT nu ru This Project has three experiments. Please note that you can submit the responses only once. Due date is Friday December 2, 2016 by 11:59 PM. What is your first name? What is your last name? What is your last name? Experiment-1 ud u Shuffle a deck of cards at least for 5 times and then lay out three cards face up. This is done without replacement. (i.e., there will be 51 cards for drawing the second card and 50 cards for drawing the third card and also the probability of drawing a second card as red, given the first card is black is 26/51 = 0.510, etc). Record the number of red cards or black cards. What are the possible different outcomes you can expect to see in each trail? = = = = {RRR, RBR, RRB, BRR, BBR, BRB, RBB, BBB} {R, B} {52 Outcomes} {RRR, RRB, RBR, RBB, BBB} tM S S S S 0.0111 0.5 0.245 0.111 en What is n(S)? ka What is the probability that you will find no red card in a single trail of your experiment? Give your answer limited to 3 decimal places. V 52 24 8 ALL OF THE ABOVE What are the minimum and maximum number of red cards possible to be faced up in this experiment? Min Min Min Min Min = = = = 1 1 0 0 0 and and and and and Max Max Max Max Max = = = = = 5 3 5 3 26 Venkateswara Rao Mudunuru Fall 2016 P a g e |2 Instructor: Venkateswara Rao Mudunuru In your experiment, what is the probability that you will have at least two red cards in a single trail? Give your answer limited to 3 decimal places. nu ru What is the probability that you will see at least one red face card in a single trail? Give your answer limited to 3 decimal places. What is the probability that you will have all black cards in a single trail of your experiment? Give your answer limited to 3 decimal places. Experiment-2 Consider EXAM-1 points out of 120 points. Given that the EXAM-1 scores of our class of total 400 students this semester is normally distributed with mean 95 and standard deviation 5. ud u What is the probability that a randomly selected student will have more than 95 points on this EXAM-1? tM 1 0.479 0.5 Incomplete information How many students from the class will have scores between 90 and 105 points? 300 362 326 236 ka What is your score on EXAM-1 out of 120 points? What is the corresponding z-value for your score? Give 2 decimal places. en What is the area covered above the z-score you calculated for your EXAM-1 score? Give 3 decimal places. Is your EXAM-1 score beyond or below 3 standard deviations from the mean? V Yes No Maybe Suppose you wanted to estimate the average of EXAM-1 score for the entire class and hence you wanted to collect 10 scores of your class mates (including you). Say the collected scores from 9 students taking class with you and the scores are as follows: 105, 91, 52, 116, 100, 95, 98, 109, 96. Please include your EXAM-1 score to these 9 scores and make it a total count of 10 scores. What is the average of these 10 scores? Give 2 decimal places. Venkateswara Rao Mudunuru Fall 2016 P a g e |3 Fall 2016 STA 2023 Fall 2016 PROJECT Fall 2016 STA 2023 Fall 2016 PROJECT Instructor: Venkateswara Rao Mudunuru Sample Mean Point Estimate of Population Mean X-bar All the above What is the margin of error in this case? nu ru What is the mean you calculated called as? What is the corresponding z-score for the average you computed for the 10 students? Give 2 decimal places. ud u What is the area covered above the z-score you calculated for the average of EXAM-1 scores of these 10 students? Give 3 decimal places. Compute and report 90% confidence interval for true mean of exam-1 scores. Give 2 decimal places for lower and upper limits in an ordered pair form. tM Compute and report 95% confidence interval for true mean of exam-1 scores. Give 2 decimal places for lower and upper limits in an ordered pair form. Experiment-3 en ka In the sample of 10 student scores (please include your exam-1 score to these 9 scores to make it 10 count) 105, 91, 52, 116, 100, 95, 98, 109, 96, clearly there is at least 1 student who failed the exam. What is the estimated proportion of fail scores from these 10 scores? Note: If you are less than 60%, i.e. less than 72 points out of 120, you are considered failed. If your score is below 72, then your count of failures is 2 in this sample, otherwise it is 1. What is the maximum margin of error for the estimate of proportions in this case? Assume normality and use 90% confidence level. V 0.025 0.208 0.156 0.033 Assuming normality, compute 90% confidence interval for true proportions of failed students. (0.075, 0.125) (-0.056, 0.256) (-0.008, 0.408) (0.167, 0.233) Venkateswara Rao Mudunuru Fall 2016 P a g e |4 Fall 2016 STA 2023 Fall 2016 PROJECT Instructor: Venkateswara Rao Mudunuru What is the maximum margin of error for the estimate of proportions in this case? Assume normality and use 95% confidence level. nu ru 0.186 0.248 0.029 0.039 Assuming normality, compute 95% confidence interval for true proportions of failed students. ud u (-0.086, 0.286) (-0.048, 0.448) (0.071, 0.129) (0.161, 0.239) V en ka tM Remember: YOU MUST SUBMIT THE ANSWERS ONLINE IN THE LINK GIVEN ON CANVAS ANNOUNCEMENTS. Venkateswara Rao Mudunuru Fall 2016 P a g e |5