252x0612 10 3 06 Open in Print Layout format ECO252 QBA2 FIRST HOUR EXAM October 17 18 2005 Version 2 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 7 7 5 1 P 6 00 x 7 00 2 P x 10 22 3 P 17 5 x 0 4 x 04 Do not try to use the t table to get this 1 252x0612 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 1 2 3 4 5 6 7 8 9 x x2 5 35 28 6225 5 68 32 2624 5 35 28 6225 5 47 29 9209 5 31 28 1961 5 49 30 1401 5 41 29 2681 5 48 30 0304 5 42 29 3764 48 96 266 4394 2 252x0612 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 above f 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 1070 b 740 c 535 d 330 e None of the above f 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 and found 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 2655 b 2654 c 665 d 664 e 50 f 40 g 20 h None of the above 4 An entrepreneur is considering the purchase of a coin operated laundry The present owned claims that 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 3 252x0612 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 x b The proportion of incomes that are above the sample median x 50 c The number of incomes in the sample that are above 30000 d The sample mean x 2 e The sample mean x and the sample variance s f The sample median x 50 2 g The sample variance s 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 4 252x0612 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 01 b Exactly 02 c Between 025 and 01 d Between 05 and 02 e Between 01 and 005 f Between 02 and 01 g Exactly 99 h Exactly 98 i Between 975 and 99 j Between 95 and 98 k Between 98 and 99 l None of the above Show your answer 20 5 252x0612 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 H 0 p 45 H1 p 45 b H 0 p 45 H1 p 45 c H 0 p 45 H1 p 45 d H 0 p 45 H1 p 45 e H 0 p 45 H1 p 45 f H 0 p 45 H1 p 45 g H 0 p 45 H1 p 45 h None of the above Put in …
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