Last name: Enter your LETTER answers HERE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 First name: Note: When done, using your last name and firstname, save THIS FILE as, E270Lastname Firstname HW4 (No space between E270 and Last name) E-mail to stowfig@iupui.edu as an attachment. Example: E270Smith Adam HW4 E270 Smith Adam HW4 YES NO PAY ATTENTION Questions 1-3 are based on the following "POPULATION" data (N = 72): 132 85 148 166 59 141 174 40 74 57 92 103 158 45 159 49 101 187 157 173 101 76 91 49 192 128 50 59 84 96 112 200 137 115 161 97 168 141 195 192 94 52 189 180 49 142 72 139 1 a b c d 2 175 97 118 134 153 50 88 96 112 183 138 78 133 112 154 77 145 110 189 184 181 164 143 116 If sampling is done without replacement, the number of possible samples of size n = 6 from the above population is __________ 148,426,963 156,238,908 162,488,464 168,988,003 A random sample of size n = 6 is selected. The data in the highlighted cells above are shown below. x 59 112 45 115 50 141 a b c d The mean and variance of this sample are: xx s 87 2060.5 87 1648.4 84 2060.5 84 1648.4 a b c d For the sample means computed from the number of random samples determined in question 1, the expected value or mean of sample means is ______. Use Excel rather than your calculator to do the calculations. 114.90 117.30 119.70 122.10 3 Questions 4-8 are based on the following: The mean cost of getting a four-year college degree in a certain region of the country is $55,800 with a standard deviation of $8,700. Assume costs are normally distributed. 4 The fraction of costs in this region that fall within $5,000 of the mean cost is? a 0.5284 b 0.5034 c 0.4648 d 0.4314 5 a b c d What fraction of sample means from samples of size n = 16 graduates fall within $5,000 from the population mean? 0.9494 0.9590 0.9786 0.9982 a b c d In repeated sampling of n = 25 graduates, what fraction of sample means would fall within $3,000 from the population mean? 0.8963 0.9146 0.9329 0.9515 6 7 a b c d In repeated sampling of n = 25 graduates, the interval which contains the middle 95% of sample mean costs is: xx = ______, xx = ______ $52,390 $59,210 $52,946 $58,654 $53,573 $58,027 $53,990 $57,610 a b c d In another region 10% of the xx values from samples of size n = 25 are under $49,500 and 10% are over $55,500. From this sampling distribution information we can conclude that the population mean cost of a four-year college degree is = _______ and the population standard deviation is = ______. $53,000 $10,607 $52,500 $10,607 $53,000 $11,719 $52,500 $11,719 8 Questions 9-12 are based on the following: The mean annual Medicare spending per enrollee is $11,700 with a standard deviation of $3,250. Answer questions 9-12 based on the sampling distribution of xx for random samples of size n = 90 enrollees. 9 The fraction of sample means falling within $600 from the population mean is ______. a 0.9356 b 0.9198 c 0.8904 d 0.8530 10 a b c d 11 a b c d 95% of all xx values from samples of size n = 90 deviate from the population mean of $11,700 by no more than $______. $798 $671 $562 $439 In repeated sampling of n = 90 enrollees, the middle interval which includes the middle 95% of sample mean spending is: xx = ______, xx = ______ $11,029 $12,371 $11,138 $12,262 $11,261 $12,139 $11,323 $12,077 12 a b c d In the previous question, to reduce the margin of error such that the middle 95% of all sample means deviate from the population mean by no more than $250, the minimum sample size is ______. 710 690 670 650 The following binary data represent the students taking E270, where "1" is for students who are business majors and "0" for other majors. 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 13 a b c d 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 If we take repeated samples of size n = 40 from this population of E270 students, the expected value of sample proportions would be ______. Use Excel!! 0.821 0.783 0.761 0.758 Questions 14-17 are based on the following information Among all adult Indiana residents 85% are high school graduates. Answer questions 14-17 based on the sampling distribution of px for random samples of n = 520 Indiana residents. 14 The fraction of sample proportions obtained from samples of size n = 520 that fall within 0.04 (4 percentage points) from the population proportion is _________. a 0.9476 b 0.9742 c 0.9892 d 0.9938 15 a b c d 16 a b c d 17 a b c d The fraction of sample proportions obtained from samples of size n = 750 that fall within 0.03 (3 percentage points) from is _________. 0.9792 0.9452 0.9232 0.8764 The lower and upper ends of the interval which contains the middle 95% of all sample proportion obtained from samples of size n = 600 are: px = _______, px = _______ 0.835 0.865 0.831 0.869 0.821 0.879 0.812 0.888 In the previous question, in order the obtain a margin of error of 0.02 (MOE = 0.02) for the middle interval that contains the middle 95% of all sample proportions, the minimum sample is: n = ______. 1225 1245 1265 1285 Questions 18-20 are based on the following information Just before a mayoral election a local newspaper polls 420 voters in an attempt to predict the winner. Suppose that the candidate Johnny Comlately has 48% of the votes in a two-way race. 18 What is the probability that the newspaper's sample will predict Johnny Comlately winning the election? a 0.2709 b 0.2061 c 0.1539 d 0.1251 19 a b c d In repeated polling of n = 420 voters, 95% of sample proportions would deviate from = 0.48, in either direction, by no more than ______ (or _____ percentage points). 0.055 0.048 0.042 0.034 20 a b c d In order to make the probability of wrongly predicting victory at most 5%, the minimum number of voters to be included in the sample should be n = ______? 1068 1482 1679 1895 -3.8 0.0002919 -3.6 0.0006119 -3.4 0.0012322 -3.2 0.0023841 -3 0.0044318 -2.8 0.0079155 -2.6 0.013583 -2.4 0.0223945 -2.2 0.0354746 -2 0.053991 -1.8 0.0789502 -1.6 0.1109208 -1.4 0.1497275 -1.2 0.1941861 -1 0.2419707 -0.8 0.2896916 -0.6 0.3332246 -0.4 0.3682701 -0.2 0.3910427 0 0.3989423 0.2 0.3910427 0.4 0.3682701 0.6 0.3332246 0.8 0.2896916 1 0.2419707 1.2 0.1941861 1.4 0.1497275 1.6 0.1109208 1.8 0.0789502 2 0.053991 2.2 0.0354746 2.4 0.0223945 2.6 0.013583 2.8 0.0079155 3 0.0044318 3.2 0.0023841 3.4 0.0012322 3.6 0.0006119 3.8 0.0002919 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 0 0 19