252y0511 2/17/05 (Open in ‘Print Layout’ format) ECO252 QBA2 Name ________________ FIRST HOUR EXAM Hour of class registered _____ February 28 2005 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. 6,5.1~ Nx1. 00.210 xP 2. 50.100.7 xP3. 22.10xP4. 08.x1252y0511 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 2x 1 74.88 5607.0144 2 75.86 5754.7396 3 74.81 5596.5361 4 74.28 5517.5184 5 74.35 5527.9225 6 73.41 5389.0281 7 74.66 5574.1156Sum 522.25 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)2252y0511 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 levela) A type one error has been committedb) A type two error has been committedc) The null hypothesis is rejectedd) The alterative hypothesis is rejectede) 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]3252y0511 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)75:0Hand 75:1Hb)75:0Hand 75:1Hc)75:0Hand 75:1Hd)75:0Hand 75:1He)75:0Hand 75:1Hf)75:0Hand 75:1Hg) 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]4252y0511 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)5000:0Hand 5000:1Hb)5000:0pHand 5000:1pHc)32.:0pHand 32.:1pHd)25.:0pHand 25.:1pHe)25.:0Hand 25.:1Hf)5000:0Hand 5000:1H[16]8. 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 pbe the proportion with incomes above $40000. Our null hypotheses include (3):a)40000:0Hb)40000:0Hc)5.0:0pHd)5.0:0pHe)5.0:0pHf)40000:0Hg)40000:0Hh)5.0:0Hi)5.0:0H[19]9. 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. 5252y0511 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.6252y0511 2/17/05 (Open in ‘Print Layout’ format) ECO252 QBA2 FIRST EXAMFebruary 28 2005TAKE 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 youdo helps, and grades wrap around) . Show your work! State 0H and 1H 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 2005 Prejector model gets 35 miles per gallon on the highway. You wish to prove that the Prejector gets more than 35 mpg. 50 of the current model are tested with the results below. To personalize the data below take the last digit of your student number, divide it by 10 and add it to the numbers
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