Questions 1-4 are based on the following \"POPULATION\" data (N = 81): 331 302 1
ID: 3172974 • Letter: Q
Question
Questions 1-4 are based on the following "POPULATION" data (N = 81): 331 302 191 173 180 105 297 174 167 242 261 337 176 206 211 280 329 175 127 235 124 61 249 300 152 150 196 299 165 106 287 158 159 216 272 209 340 64 123 344 145 174 264 198 295 253 293 225 295 292 60 141 131 99 203 231 71 238 247 239 338 222 195 251 131 335 111 121 171 333 123 161 68 119 310 290 345 284 139 198 86 1 If sampling is done without replacement, the number of possible samples of size n = 6 from the above population is __________ a 278,252,668 b 292,897,545 c 308,313,205 d 324,540,216 A random sample of size n = 6 is selected. The data in the highlighted cells above are shown below. x 180 174 235 238 131 338 2 The mean of this sample is: x a 212 b 214 c 216 d 218 3 The variance of this sample is: s² a 4335.7 b 4682.5 c 5202.8 d 5406.9 4 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. a 208.62 b 216.96 c 225.64 d 234.67 5 The average speed of all vehicles on a highway is µ = 64 mph with a standard deviation of = 5 mph. A random sample of 20 vehicles is clocked. What is the probability that the sample mean will exceed 66 mph? a 0.0525 b 0.0404 c 0.0367 d 0.0220 6 In the previous question what fraction of sample means from samples of n = 20 vehicles fall within ±1 mph from the population mean speed? a 0.6266 b 0.6528 c 0.6922 d 0.7286 7 If you doubled the sample size in the previous question, what fraction of the sample means would fall within ±1 mph from the population mean speed? a 0.7108 b 0.7924 c 0.8262 d 0.8558 8 In the previous question where n = 40, the middle interval which includes the 95% of the mean speed from samples of n = 40 vehicles is, a 61.63 66.37 b 62.45 65.55 c 63.05 64.95 d 63.37 64.63 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 $48,600 with a standard deviation of $8,100. Assume costs are normally distributed. 9 The fraction of costs for all graduates in this region that fall within ±$4,000 of the mean cost is? a 0.5284 b 0.4844 c 0.4246 d 0.3758 10 What fraction of sample means from samples of size n = 16 graduates fall within ±$4,000 from the population mean? a 0.8904 b 0.9198 c 0.9398 d 0.9522 11 In repeated sampling of n = 25 graduates, the interval which contains the middle 95% of sample mean costs is: x = ______, x = ______ a $41,615 $55,585 b $42,567 $54,633 c $43,837 $53,363 d $45,425 $51,775 12 In another region 5% of the x values from samples of size n = 25 are under $48,000 and 5% are over $57,000. From this sampling distribution information we can conclude that the population mean cost of a four-year college degree is = _______. µ a $50,500 b $51,500 c $52,500 d $53,500 13 In the previous question, the population standard deviation is = ______. a $12,980 b $13,720 c $14,240 d $14,760 Questions 14-17 are based on the following: The mean annual Medicare spending per enrollee is $13,800 with a standard deviation of $3,960. Answer questions 14-17 based on the sampling distribution of x for random samples of size n = 81 enrollees. 14 The fraction of sample means falling within ±$600 from the population mean is ______. a 0.9026 b 0.8849 c 0.8675 d 0.8262 15 95% of all x values from samples of size n = 81 deviate from the population mean of $13,800 by no more than ±$______. a $939 b $903 c $862 d $790 16 In repeated sampling of n = 81 enrollees, the middle interval which includes the middle 95% of sample mean spending is: x = ______, x = ______ a $12,380 $15,220 b $12,796 $14,804 c $12,938 $14,662 d $13,010 $14,590 17 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 ±$300, the minimum sample size is ______. a 625 b 670 c 744 d 805 The following binary data represent the students taking E270, where "1" is for students who are business majors and "0" for other majors. 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 18 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!! a 0.86 b 0.82 c 0.78 d 0.75 Questions 19-22 are based on the following information Among all adult Indiana residents 84% are high school graduates. Answer questions 19-22 based on the sampling distribution of p for random samples of n = 500 Indiana adult residents. 19 What fraction of sample proportions fall under 0.82? a 0.0994 b 0.1112 c 0.1334 d 0.1601 20 The fraction of sample proportions obtained from samples of size n = 500 that fall within ±0.04 (4 percentage points) from the population proportion is _________. a 0.9498 b 0.9685 c 0.9854 d 0.9922 21 The lower and upper ends of the interval which contains the middle 95% of all sample proportions obtained from samples of size n = 950 are: p = _______, p = _______ a 0.806 0.855 b 0.817 0.863 c 0.788 0.872 d 0.779 0.881 22 In the previous question, in order to 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 = ______. a 1468 b 1401 c 1356 d 1291 Questions 23-25 are based on the following information Just before a mayoral election a local newspaper polls 450 voters in an attempt to predict the winner. Suppose that the candidate Johnny Comlately has 53% of the votes among all voters in a two-way race. 23 What is the probability that the newspaper’s sample will predict Johnny Comlately losing the election? a 0.1248 b 0.1003 c 0.0865 d 0.0695 24 In repeated polling of n = 450 voters, 95% of sample proportions would deviate from = 0.53, in either direction, by no more than ______ (or _____ percentage points). a 0.034 b 0.039 c 0.046 d 0.052 25 In order to make the probability of wrongly predicting loss at most 5%, the minimum number of voters to be included in the sample should be n = ______? a 625 b 698 c 745 d 940 Questions 1-4 are based on the following "POPULATION" data (N = 81): 331 302 191 173 180 105 297 174 167 242 261 337 176 206 211 280 329 175 127 235 124 61 249 300 152 150 196 299 165 106 287 158 159 216 272 209 340 64 123 344 145 174 264 198 295 253 293 225 295 292 60 141 131 99 203 231 71 238 247 239 338 222 195 251 131 335 111 121 171 333 123 161 68 119 310 290 345 284 139 198 86 1 If sampling is done without replacement, the number of possible samples of size n = 6 from the above population is __________ a 278,252,668 b 292,897,545 c 308,313,205 d 324,540,216 A random sample of size n = 6 is selected. The data in the highlighted cells above are shown below. x 180 174 235 238 131 338 2 The mean of this sample is: x a 212 b 214 c 216 d 218 3 The variance of this sample is: s² a 4335.7 b 4682.5 c 5202.8 d 5406.9 4 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. a 208.62 b 216.96 c 225.64 d 234.67 5 The average speed of all vehicles on a highway is µ = 64 mph with a standard deviation of = 5 mph. A random sample of 20 vehicles is clocked. What is the probability that the sample mean will exceed 66 mph? a 0.0525 b 0.0404 c 0.0367 d 0.0220 6 In the previous question what fraction of sample means from samples of n = 20 vehicles fall within ±1 mph from the population mean speed? a 0.6266 b 0.6528 c 0.6922 d 0.7286 7 If you doubled the sample size in the previous question, what fraction of the sample means would fall within ±1 mph from the population mean speed? a 0.7108 b 0.7924 c 0.8262 d 0.8558 8 In the previous question where n = 40, the middle interval which includes the 95% of the mean speed from samples of n = 40 vehicles is, a 61.63 66.37 b 62.45 65.55 c 63.05 64.95 d 63.37 64.63 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 $48,600 with a standard deviation of $8,100. Assume costs are normally distributed. 9 The fraction of costs for all graduates in this region that fall within ±$4,000 of the mean cost is? a 0.5284 b 0.4844 c 0.4246 d 0.3758 10 What fraction of sample means from samples of size n = 16 graduates fall within ±$4,000 from the population mean? a 0.8904 b 0.9198 c 0.9398 d 0.9522 11 In repeated sampling of n = 25 graduates, the interval which contains the middle 95% of sample mean costs is: x = ______, x = ______ a $41,615 $55,585 b $42,567 $54,633 c $43,837 $53,363 d $45,425 $51,775 12 In another region 5% of the x values from samples of size n = 25 are under $48,000 and 5% are over $57,000. From this sampling distribution information we can conclude that the population mean cost of a four-year college degree is = _______. µ a $50,500 b $51,500 c $52,500 d $53,500 13 In the previous question, the population standard deviation is = ______. a $12,980 b $13,720 c $14,240 d $14,760 Questions 14-17 are based on the following: The mean annual Medicare spending per enrollee is $13,800 with a standard deviation of $3,960. Answer questions 14-17 based on the sampling distribution of x for random samples of size n = 81 enrollees. 14 The fraction of sample means falling within ±$600 from the population mean is ______. a 0.9026 b 0.8849 c 0.8675 d 0.8262 15 95% of all x values from samples of size n = 81 deviate from the population mean of $13,800 by no more than ±$______. a $939 b $903 c $862 d $790 16 In repeated sampling of n = 81 enrollees, the middle interval which includes the middle 95% of sample mean spending is: x = ______, x = ______ a $12,380 $15,220 b $12,796 $14,804 c $12,938 $14,662 d $13,010 $14,590 17 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 ±$300, the minimum sample size is ______. a 625 b 670 c 744 d 805 The following binary data represent the students taking E270, where "1" is for students who are business majors and "0" for other majors. 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 18 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!! a 0.86 b 0.82 c 0.78 d 0.75 Questions 19-22 are based on the following information Among all adult Indiana residents 84% are high school graduates. Answer questions 19-22 based on the sampling distribution of p for random samples of n = 500 Indiana adult residents. 19 What fraction of sample proportions fall under 0.82? a 0.0994 b 0.1112 c 0.1334 d 0.1601 20 The fraction of sample proportions obtained from samples of size n = 500 that fall within ±0.04 (4 percentage points) from the population proportion is _________. a 0.9498 b 0.9685 c 0.9854 d 0.9922 21 The lower and upper ends of the interval which contains the middle 95% of all sample proportions obtained from samples of size n = 950 are: p = _______, p = _______ a 0.806 0.855 b 0.817 0.863 c 0.788 0.872 d 0.779 0.881 22 In the previous question, in order to 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 = ______. a 1468 b 1401 c 1356 d 1291 Questions 23-25 are based on the following information Just before a mayoral election a local newspaper polls 450 voters in an attempt to predict the winner. Suppose that the candidate Johnny Comlately has 53% of the votes among all voters in a two-way race. 23 What is the probability that the newspaper’s sample will predict Johnny Comlately losing the election? a 0.1248 b 0.1003 c 0.0865 d 0.0695 24 In repeated polling of n = 450 voters, 95% of sample proportions would deviate from = 0.53, in either direction, by no more than ______ (or _____ percentage points). a 0.034 b 0.039 c 0.046 d 0.052 25 In order to make the probability of wrongly predicting loss at most 5%, the minimum number of voters to be included in the sample should be n = ______? a 625 b 698 c 745 d 940Explanation / Answer
1)
the number of possible samples of size n = 6 is 81C6 = 324540216
2)
The mean of the sample is:
= (180 + 174 + 235 + 238 + 131 + 338) / 6
= 1296 / 6 = 216
3)
The variance of the sample is: 4335.7
4)
the expected value or mean of sample means is 216
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