Christian, Ryan, Liz, and Grace, Here are your scores on the Chapter 9 project from last week. Let me know if you have any questions. A) - D) for the two data sets: 60/60 (all very good!) E) OK -- the data in the first case was supposed to come from a uniform distribution on the interval 0 to 1, but the random number generator in the RAND() function can produce funny results sometimes. The histograms will "usually" be less bimodal than yours -- the 200 numbers would usually be more nearly equally distributed over the 10 intervals. 2/2 F) 2/2 G) Good -- exactly right 2/2 H) 1/2 Yes, but why is that true? Think about the formula for computing the overall average and how that relates to the average of the row averages. I) 2/2 OK -- I was thinking that a "truly random" sample of 10 numbers, for instance could come from any 10 of the cells in the block, not just the 10 cells in one of the rows. You're looking at subsets of a special form if you only take the 10 cells in one row. J) 1/2 Yes, but why again? The idea is that if you took 20 "truly" random samples of size 10 from the population, you might in fact be getting the same number more than once, so the average of the sample means could be different from the overall mean. Total: 70/72 (Very good!) &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Kyle, Lily, Emily, Here are your scores on the Chapter 9 project from last week. Let me know if you have any questions. A) - D) for the two data sets: 60/60 (all very good!) E) OK -- the data in the first case was supposed to come from a uniform distribution on the interval 0 to 1, but the random number generator in the RAND() function can produce funny results sometimes. The histograms will "usually" be less bimodal than yours -- the 200 numbers would usually be more nearly equally distributed over the 10 intervals. 2/2 F) 1/2 -- If you look closely, you'll see that the distributions of the row averages look pretty much the same for both data sets, even though the overall distributions are pretty different. The first one is close to uniformly distributed, the second one is much more "humped" in the middle. G) OK -- 2/2 H) 1/2 Yes, but why is that true? Think about the formula for computing the overall average and how that relates to the average of the row averages. The average of the row averages will ALWAYS be the same as the overall average. I) 1/2 OK -- I was thinking that a "truly random" sample of 10 numbers, for instance could come from any 10 of the cells in the block, not just the 10 cells in one of the rows. You're looking at subsets of a special form if you only take the 10 cells in one row. J) 1/2 Yes, but why again? The idea is that if you took 20 "truly" random samples of size 10 from the population, you might in fact be getting the same number more than once, so the average of the sample means could be different from the overall mean. Total: 68/72 (Good!) &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Angel, Connor, Matt, and Eve, Here are your scores on the Chapter 9 project from last week. Let me know if you have any questions. A) - D) for the two data sets: 60/60 (all very good!) E) OK -- the data in the first case was supposed to come from a uniform distribution on the interval 0 to 1; the second comes from a normal distribution. 2/2 F) 1/2 -- If you look closely, you'll see that the distributions of the row averages look pretty much the same for both data sets, even though the overall distributions are pretty different. The first one is close to uniformly distributed, the second one is much more "humped" in the middle. G) I can't reall tell what you are saying here. Be sure you are distinguishing between the number of numbers in the sample and the number of samples. The pattern you should see is that the SD goes down as the size of the sample increases. overall SD > SD of row means > SD of column means 1/2 H) 2/2 Yes. I) 2/2 OK -- I was thinking that a "truly random" sample of 10 numbers, for instance could come from any 10 of the cells in the block, not just the 10 cells in one of the rows. You're looking at subsets of a special form if you only take the 10 cells in one row. J) 1/2 Not necessarily. The idea is that if you took 20 "truly" random samples of size 10 from the population, you might in fact be getting the same number more than once, so the average of the sample means could be different from the overall mean since you might not be getting all 200 of the numbers. Total: 69/72 (Good!) &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Genevieve, Logan, and Madison, Here are your scores on the Chapter 9 project from last week. Let me know if you have any questions. A) - D) for the two data sets: 60/60 (all very good!) E) OK -- the data in the first case was supposed to come from a uniform distribution on the interval 0 to 1; the second comes from a normal distribution. 2/2 F) 1/2 -- If you look closely, you'll see that the distributions of the row averages look pretty much the same for both data sets, even though the overall distributions are pretty different. The first one is close to uniformly distributed, the second one is much more "humped" in the middle. G) I can't reall tell what you are saying here. Be sure you are distinguishing between the number of numbers in the sample and the number of samples. The pattern you should see is that the SD goes down as the size of the sample increases. overall SD > SD of row means > SD of column means 1/2 H) 1/2 Not exactly. They will ALWAYS be exactly the same because taking the average of the row averages in effect adds together all of the numbers and divides the sum by 10, then by 20. The result is the same as adding all the numbers, then dividing the overall total by 200. I) 1/2 I was thinking that a "truly random" sample of 10 numbers, for instance could come from any 10 of the cells in the block, not just the 10 cells in one of the rows. You're looking at subsets of a special form if you only take the 10 cells in one row. J) 1/2 Not necessarily. The idea is that if you took 20 "truly" random samples of size 10 from the population, you might in fact be getting the same number more than once, so the average of the sample means could be different from the overall mean since you might not be getting all 200 of the numbers. Total: 67/72 (Good!)