252x0612 10/3/06 (Open in ‘Print Layout’ format) ECO252 QBA2 Name ________________ FIRST HOUR EXAM Hour of class registered _____ October 17-18 2005 Class attended if different ____ Version 2Show your work! Make Diagrams! Exam is normed on 50 points. Answers without reasons are not usually acceptable.I. (8 points) Do all the following. 5.7,7~ Nx1. 00.700.6 xP2. 22.10xP3. 05.17 xP 4. 04.x(Do not try to use the t table to get this.)1252x0612 10/3/06 (Open in ‘Print Layout’ format)II. (5 points-2 point penalty for not trying part a.) In order not to violate the truth in labeling law a teabag must contain at least 5.5 oz of tea. A sample of 9 items is taken from a large number of tea bags. The data below is found. (Recomputing what I’ve done for you is a great way to waste time.) b) and d) require statistical tests.a. Compute the sample standard deviation,s, of the waiting times. Show your work! (2)b. Is the population mean significantly below 5.5 (Use a 95% confidence level)? Show your work! (3) [13]c. (Extra Credit) Find an approximate p value for your null hypothesis. (2)d. Assume that the population standard deviation is 0.10 and create a 92% confidence interval for the mean. (2)e. (Extra Credit) Given the data, is 0.10 a reasonable value for the population standard deviation? Row x 2x 1 5.35 28.6225 2 5.68 32.2624 3 5.35 28.6225 4 5.47 29.9209 5 5.31 28.1961 6 5.49 30.1401 7 5.41 29.2681 8 5.48 30.0304 9 5.42 29.3764 48.96 266.43942252x0612 10/3/06 (Open in ‘Print Layout’ format)III. Do as many of the following problems as you can.(2 points each unless marked otherwise adding to 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. Which of the following is a Type 1 error?a) Rejecting the null hypothesis when the null hypothesis is false.b) Rejecting the null hypothesis when the null hypothesis is true.c) Not rejecting the null hypothesis when the null hypothesis is true.d) Not rejecting the null hypothesis when the null hypothesis is false.e) All of the abovef) None of the above.2. A librarian provides a confidence interval estimate for the mean number of books checked out daily. The estimate is 330 to 740. The point estimate that this interval is based on is.a) 1070b) 740c) 535d) 330e) None of the abovef) There is not enough information to tell.3. (BLK8.30) If we want a 99% confidence interval for the average income of in a town, and the population standard deviation is known to be $1000. We have taken a sample of size 50 earlier andfound that the sample mean is $20000. What sample size should we take if the width of the interval is to be no more than $100?a) 2655b) 2654c) 665d) 664e) 50f) 40g) 20h) None of the above.4. An entrepreneur is considering the purchase of a coin-operated laundry. The present owned claimsthat over the past 6 years the average daily income was $700. A sample is taken of daily revenue over a period of 28 days. Statistics are computed from the sample. If we want to test the statement that the mean is $700, which of the following tests is most appropriate? (1 point)a)z-test of a population mean.b)z-test of a population proportion.c)t-test of a population mean.d)2-test of a population variance. e)F-test.f) All of the above could be used.g) We do not have enough information. [7]3252x0612 10/3/06 (Open in ‘Print Layout’ format)5. We are trying to estimate the median income in a region. We wish to test if the median is over $30000. We do not know the population variance. We can compute a statistic or statistics from a sample of 27 incomes. To do this test, the statistic or statistics we need is (are) a) The proportion of incomes that are above the sample mean, .xb) The proportion of incomes that are above the sample median 50.x.c) The number of incomes in the sample that are above $30000.d) The sample mean, .xe) The sample mean, x and the sample variance .2sf) The sample median 50.x.g) The sample variance .2s [9]6. A restaurant company only opens restaurants in areas with a mean family income above $45000. The company takes a sample of 144 families in Hotzeplotz and finds a sample mean income of $46396 with a sample standard deviation of $5400. Should they open? 05.a) State your null and alternative hypotheses. (1) b) Test your hypothesis in a) by finding a critical value for the sample mean. Can we say that the result of the sample is above $45000? Why? (3)c) Do a 2-sided confidence interval for the mean. (2)d) Do a 2-sided confidence interval for the variance. (2) [17]e) (Extra credit) Explain in as much detail as reasonable how you would find a confidence interval for the median. (2) 4252x0612 10/3/06 (Open in ‘Print Layout’ format)7. Return to the problem in Question 6. Let’s say that the sample mean income of $46396 and the sample standard deviation of $5400 come from a sample of 81. Assume that your null hypothesis is correct and that you get a t-ratio of 2.327. What should you say that that the p-value is? (3 points) Note that showing your calculations here could get you partial credit. a) Exactly .01b) Exactly .02 c) Between .025 and .01d) Between .05 and .02e) Between .01 and .005f) Between .02 and .01g) Exactly .99h) Exactly .98 i) Between .975 and .99j) Between .95 and .98k) Between .98 and .99l) None of the above – Show your answer! [20]5252x0612 10/3/06 (Open in ‘Print Layout’ format)8. (Mann) According to a 1992 survey, 45% of workers say that they would change careers if they could. You wish to show that the proportion of workers in your company that want to change careers is below the national value. Find the correct set of hypotheses below.a)45.:45.:10pHpHb)45.:45.:10pHpHc)45.:45.:10pHpHd) 45.:45.:10pHpHe) 45.:45.:10pHpHf)45.:45.:10pHpHg)45.:45.:10pHpHh) None of the above. Put in your answer! [22]9. (Mann) According to a 1992 survey, 45% of workers say that they would change careers if they could. You wish to show that the proportion of workers in your company that want to change careers is below the national figure. Assume that your null hypothesis in 8 is correct, that you take a sample of 350 workers and that you compute the ratio
View Full Document
Unlocking...