252y0511 2 17 05 Open in Print Layout format ECO252 QBA2 FIRST HOUR EXAM February 28 2005 Name Hour of class registered Class attended if different Show your work Make Diagrams Exam is normed on 50 points Answers without reasons are not usually acceptable I 8 points Do all the following x N 1 5 6 1 P 0 x 21 00 2 P 7 00 x 1 50 3 P x 10 22 4 x 08 1 252y0511 2 17 05 Open in Print Layout format II 5 points 2 point penalty for not trying part a Mansfield A random sample is taken of the length in feet of aluminum foil rolls The following data is found Recomputing what I ve done for you is a great way to waste time x x2 1 2 3 4 5 6 7 Sum 74 88 75 86 74 81 74 28 74 35 73 41 74 66 522 25 5607 0144 5754 7396 5596 5361 5517 5184 5527 9225 5389 0281 5574 1156 38966 8747 a Compute the sample standard deviation s of the waiting times Show your work 2 b Compute a 99 confidence interval for the population mean 2 c Is the population mean significantly different from 75 8 ft 1 2 252y0511 2 17 05 Open in Print Layout format III Do all of the following Problems 18 points Show your work except in multiple choice questions Actually it doesn t hurt there either If the answer is None of the above put in the correct answer 1 When a p value is smaller than a significance level a A type one error has been committed b A type two error has been committed c The null hypothesis is rejected d The alterative hypothesis is rejected e The critical value is correct 2 The t distribution should be used when the parent underlying population a Is Normal the population standard deviation is unknown and we are testing a mean b Is Normal the population standard deviation is known and we are testing a mean c Is Normal the mean of the population is unknown and we are testing a mean d Is binomial and we are testing for a proportion e The t distribution should be used in all of these cases 3 The Normal distribution can be used in all of the cases below except when a We are testing a mean the population standard deviation is unknown and the sample is large b We are testing a proportion and the sample is large c We are testing a variance and the sample is large d We are testing the mean of a Poisson distribution and the sample is large e All of the above are cases when the Normal distribution can be used 6 4 Lange The state wants to estimate the proportion of the labor force that was unemployed in North Hotzeplotz and wants to be 99 confident that their estimate is within 5 written 0 05 of the population proportion If the proportion is probably about 15 how large a sample is needed 3 9 3 252y0511 2 17 05 Open in Print Layout format 5 I wish to do a test to see if the average level of satisfaction of my employees is above 75 on a zero to 100 scale I take a survey of 30 of my 100 employees and get a mean of 76 I assume that the data is Normally distributed with a standard deviation of 8 What are my null and alternate hypotheses a b c d e H 0 75 and H 1 75 H 0 75 and H 1 75 H 0 75 and H 1 75 H 0 75 and H 1 75 H 0 75 and H 1 75 H 0 75 and H 1 75 f g None of the above 6 I wish to do a test to see if the average level of satisfaction of my employees is above 75 on a zero to 100 scale I take a survey of 30 of my 100 employees and get a mean of 76 I assume that the data is Normally distributed with a standard deviation of 8 Assume that your null and alternate hypotheses in question 5 are correct and that your confidence level is 92 Find a critical value for the sample mean Show clearly what formulas you are using 3 14 4 252y0511 2 17 05 Open in Print Layout format 7 Dummeldinger A movie rental chain is considering opening a new outlet The corporation will open an outlet only if more than 5000 out of the 20000 households in the area have DVD players It randomly selects 300 households and finds that 96 have DVD players What are our null and alternative hypotheses a H 0 5000 and H 1 5000 b c d e f 8 16 We wish to determine if the median income in an area exceeds 40000 A random sample of 250 households was selected 104 had incomes above 40000 Let p be the proportion with incomes above 40000 Our null hypotheses include 3 a H 0 40000 b c d e f g h i 9 H 0 p 5000 and H 1 p 5000 H 0 p 32 and H 1 p 32 H 0 p 25 and H 1 p 25 H 0 25 and H 1 25 H 0 5000 and H 1 5000 H 0 40000 H 0 p 0 5 H 0 p 0 5 H 0 p 0 5 H 0 40000 H 0 40000 H 0 0 5 H 0 0 5 19 We wish to determine if the median income in an area exceeds 40000 A random sample of 250 households was selected 104 had incomes above 40000 Let p be the proportion with incomes above 40000 Assume that your null hypotheses in 8 are correct and test the hypothesis a Using a test ratio and a p value 2 b Using a critical value for x p s or the median as appropriate 2 c Using a confidence interval 2 3 or 5 depending on your level of chutzpah d Extra Credit Redo a b or c assuming that the sample of 250 came from a population of 2000 5 252y0511 2 17 05 Open in Print Layout format Blank page for calculations If you use any other paper for calculations turn it in it can only help you 6 252y0511 2 17 05 Open in Print Layout format ECO252 QBA2 FIRST EXAM February 28 2005 TAKE HOME SECTION Name Student Number and class IV Do at least 3 problems at least 7 each or do sections adding to at least 20 points Anything extra you do helps and grades wrap around Show your work State H 0 and H 1 where appropriate You have not done a hypothesis test unless you have stated your hypotheses run the numbers and stated your conclusion Use a 95 confidence level unless another level is specified Answers without reasons are not usually acceptable 1 Dummeldinger You are an automobile manufacturer and the EPA has just estimated that your …
View Full Document
Unlocking...