5 Questions on Sample Variance - Final Examination | QMST 2333, Exams of Statistics

Download 5 Questions on Sample Variance - Final Examination | QMST 2333 and more Exams Statistics in PDF only on Docsity! FINAL Exam QMST 2333 SPRING 2010 Last Name/ First Name Q1) 15 pts You work at the running store Red. You have followed 20 runners for a year. In order to protect the privacy of individuals they have been assigned ID numbers which are recorded below. The random variable X, is defined as the # of shoes that an individual with the corresponding ID number has bought. If it is of interest, you know the following about X. Sum of X is 95. Sample variance is 6.42. The 50th percentile of X is 5. a) Find the mean of X. b) Find the sample standard deviation of X. c) Find the median of X. d) Find the mode of X. e) What is the range of X. ID Number # of Shoes 1 1 2 5 3 2 4 5 5 9 6 3 7 9 8 6 9 2 10 4 11 3 12 2 13 8 14 2 15 6 16 1 17 5 18 3 19 3 20 6 Q2) 20 pts Within the context of question number 1. You would like to know whether gender has an effect on the number of shoes that are bought per year. Using Excel Functions you group the data based on gender and grouped number of shoes bought. Alpha = 0.05 a) What is the name of the analysis (hypothesis test) you need to do in order to establish whether these two variables are independent? b) Do this analysis below as we have done in class. Number of Shoes Bought 1-3 4-6 7-9 Gender Male 6 4 2 Female 4 3 1 Q3) 20 pts 500 1000 1500 2000 2500 3000 -40000 -20000 0 20000 40000 Size Residual Plot Size R e si d u al s THESE ARE THE QUESTIONS YOU NEED TO ANSWER a) Find the correlation between size and price (correlation = r) b) Find the coefficient of determination (coefficient of determination = r^2) c) Does the variable size have an effect on the estimate of price? (reason) d) If I increase the size of my home by 1 square foot how much should I expect my house price to increase/decrease? e) What is the coefficient of the intercept? f) Find the EXPECTED price of a home that is 1800 square feet. g) Fill in the empty cells below ANOVA Df SS MS F Significance F Regr. 84566797281 2.75894E-81 Residual 82223164669 Total 517 166789961950 h) Look at the Size Residual Plot on the page above. What assumptions can you visually test by looking at this plot? Are these assumptions met, why? Q5) Answer a-d as TRUE/FALSE, You need to also give the reasoning behind your answer or no points given. 15pts Assume you do a hypothesis test to test whether the average tonnage (unit of weight) of apples per tree in one particular patch (say Patch number 1) of your orchard is greater than in another patch (say Patch number 2). You know every year there will be some variance of the number of apples produced due to factors that are not possible to be controlled. Therefore you decide to look at the last 50 years’ historical records for which the tonnages from both patches were recorded. The sample mean tonnage per tree was 0.4 ton per tree in patch number one and 0.35 in the other patch. The pooled standard deviation was .05. There were 50 trees that you were able to track in each patch for these 50 years. Alpha = 0.05, p is approx 0.0001 a) You know the probability of committing a type 1 error. b) You found out that the mean tonnage per tree in patch 1 is greater than the mean tonnage per tree in patch 2, such that you have no doubts as to this conclusion. c) You build an independent samples t-test 95% confidence interval from the above given data. Do you know as a result the probability that the population mean differences will be between those confidence intervals?