252y061t 10 10 06 Open in Print Layout format ECO252 QBA2 FIRST EXAM October 11 12 2006 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 usually are not acceptable Neatness and clarity of explanation are expected This must be turned in when you take the in class exam 1 Moore Notz You are thinking that it may be desirable to start a wellness program for your large company You are told that the company will only start such a program if you can show that the blood pressure of a group of mid level executives is above normal The individuals are all between 35 and 44 years old and US statistics show that mean systolic blood pressure for men in that age range is 128 You take a sample of 72 executives and get the following results x 139 60 136 21 114 18 128 45 120 68 127 51 128 07 161 43 161 09 130 61 130 15 154 74 126 29 124 48 117 51 138 22 169 05 116 14 182 53 141 96 122 14 163 18 124 61 100 03 130 77 140 35 158 74 120 02 137 23 127 22 141 54 105 67 149 55 109 52 131 40 126 54 118 77 141 15 150 30 126 93 144 71 127 32 136 69 125 06 135 21 149 44 133 89 118 37 124 80 133 00 131 74 135 69 169 61 126 71 107 30 122 73 125 35 152 64 109 62 116 59 132 00 117 84 120 01 117 47 145 25 159 94 112 34 145 10 119 39 127 67 117 97 112 40 To personalize the data below take the last digit of your student number divide it by 10 and add it to the numbers below If the last digit of your student number is zero add 1 00 Label the problem Version 1 Version 2 Version 10 according to the number that you used For example Seymour Butz s student number is 976502 so he will add 0 20 and change the data to 139 80 130 81 182 73 etc but see the hint below you do not need to write down all the numbers that you are using just your computations Hint if you use the computational formula For the original numbers n 72 x 9528 41 and x 2 1280763 7 If you add a quantity a to a column of numbers x a x na x a 2 x 2 2a x na 2 Assume that the Normal distribution applies to the data and use a 99 confidence level a Find the sample mean and sample standard deviation of the incomes in your data showing your work 1 Your mean should be fairly near 132 and your sample standard deviation should be near 16 or 17 b State your null and alternative hypotheses 1 c Test the hypothesis using a test ratio 1 d Test the hypothesis using a critical value for a sample mean 1 e Test the hypothesis using a confidence interval 1 f Find an approximate p value for the null hypothesis 1 g On the basis of your tests will you get a wellness program Why 1 h How do your conclusions change if the sample of 72 is taken from a population of 200 2 i Assume that the Normal distribution does not apply and using your data test that the median is above 128 3 12 j Extra credit Use your data to get an approximate 90 2 sided confidence interval for the median 252y061t 10 10 06 Open in Print Layout format 2 Once again assume that the Normal distribution applies but assume a population standard deviation of 16 and that we are testing whether the mean is above 128 90 confidence level a State your null and alternative hypotheses 1 b Find a p value for the null hypothesis using the mean that you found in a On the basis of your p value would you reject the null hypothesis Why 1 c Create a power curve for the test 6 20 3 Moore Notz A recent survey said that nationwide 73 of all freshman students identified being well off financially as an important lifetime goal You believe that the proportion of freshman business majors with that goal is higher than the national figure You take a survey of a random sample of 200 students and find that 152 a have being well off as an important goal where a is the second to last digit of your student number If the second to last digit of your student number is zero a 10 For example Seymour Butz s student number is 976502 so he will add 10 and say that x 152 10 162 Label your solution Version a where a is the number that you are using a Formulate your null and alternative hypotheses and do a hypothesis test with a 95 confidence level 2 b Find a p value for the null hypothesis 1 c Find the p value for the null hypothesis if x 162 a 1 c Extra credit How would your answer to a change if your sample of 200 came from a population of 300 1 d Extra credit Using a critical value of the proportion for testing your null hypothesis create a power curve for the test by using the alternate hypothesis and finding the power for values of p1 73 Up to 6 points d Assume that p 73 how large a sample would you need to estimate the proportion above that have being well off with an error of 005 2 e Use the proportion that you found in a to create a 2 sided 95 confidence interval for the proportion Does it differ significantly from 73 Why 2 28 4 Standard deviation is often a measure of reliability A manufacturer is providing a connector with a mean length of 2 5 mm and is getting complaints that the connector is often too large or too small for the intended use The previous standard deviation to the length of the part was 0 025mm but the manufacturer introduces a process that should make the standard deviation smaller A sample of 25 items is taken which yields a sample standard deviation of 0 030 a To get a take the third to last digit of your student number and multiply it by 0 001 For example Seymour Butz s student number is 976502 so he will subtract 005 and say that s 0 030 0 005 0 025 a Formulate the null and alternative hypotheses necessary to see if the goal has been achieved and test …
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