Sampling Distributions BPS chapter 11 © 2006 W.H. Freeman and Company
Parameters and statistics <ul><li>The average fuel tank capacity of all cars made by Ford is 14.7 gallons.  This value rep...
Parameters and statistics  (answer) <ul><li>The average fuel tank capacity of all cars made by Ford is 14.7 gallons.  This...
Parameters and statistics <ul><li>The fraction of all American adults who received at least one speeding ticket last year ...
Parameters and statistics  (answer) <ul><li>The fraction of all American adults who received at least one speeding ticket ...
Parameters and statistics <ul><li>The mean distance traveled in a year by a sample of truck drivers can be represented by ...
Parameters and statistics  (answer) <ul><li>The mean distance traveled in a year by a sample of truck drivers can be repre...
Sample size <ul><li>We wish to estimate the mean price,   , of all hotel rooms in Las Vegas.  The Convention Bureau of La...
Sample size  (answer) <ul><li>We wish to estimate the mean price,   , of all hotel rooms in Las Vegas.  The Convention Bu...
Law of Large Numbers <ul><li>The Law of Large Numbers says that </li></ul><ul><li>If the population is large, the estimate...
Law of Large Numbers  (answer) <ul><li>The Law of Large Numbers says that </li></ul><ul><li>If the population is large, th...
Sampling distribution <ul><li>If the first graph shows the population, which plot could be the sampling distribution of  i...
Sampling distribution  (answer) <ul><li>If the first graph shows the population, which plot could be the sampling distribu...
Sampling distribution <ul><li>Which of the following is true? </li></ul><ul><li>The shape of the sampling distribution of ...
Sampling distribution  (answer) <ul><li>Which of the following is true? </li></ul><ul><li>The shape of the sampling distri...
Sampling distribution <ul><li>True or false:  The shape of the sampling distribution of  becomes more normal the larger yo...
Sampling distribution  (answer) <ul><li>True or false:  The shape of the sampling distribution of  becomes more normal the...
Sampling distribution <ul><li>True or false:  The standard deviation of the sampling distribution of  is always less than ...
Sampling distribution  (answer) <ul><li>True or false:  The standard deviation of the sampling distribution of  is always ...
Sampling distribution <ul><li>The theoretical sampling distribution of  </li></ul><ul><li>Gives the values of  from all po...
Sampling distribution  (answer) <ul><li>The theoretical sampling distribution of  </li></ul><ul><li>Gives the values of  f...
Standard error <ul><li>What does  measure?  </li></ul><ul><li>The spread of the population. </li></ul><ul><li>The spread o...
Standard error  (answer) <ul><li>What does  measure?  </li></ul><ul><li>The spread of the population. </li></ul><ul><li>Th...
Sample size <ul><li>True or false:  If we want the mean of all possible  ‘s to equal   , then we must use a large sample ...
Sample size  (answer) <ul><li>True or false:  If we want the mean of all possible  ‘s to equal   , then we must use a lar...
Sampling distributions <ul><li>The following density curve represents waiting times at a customer service counter at a nat...
Sampling distributions  (answer) <ul><li>The following density curve represents waiting times at a customer service counte...
Central Limit Theorem <ul><li>Which is a true statement about the Central Limit Theorem? </li></ul><ul><li>We need to take...
Central Limit Theorem  (answer) <ul><li>Which is a true statement about the Central Limit Theorem? </li></ul><ul><li>We ne...
Central Limit Theorem <ul><li>True or false:  The Central Limit Theorem allows us to compute probabilities on  when the co...
Central Limit Theorem  (answer) <ul><li>True or false:  The Central Limit Theorem allows us to compute probabilities on  w...
Sampling distributions <ul><li>The following density curve shows a sampling distribution of  created by taking all possibl...
Sampling distributions  (answer) <ul><li>The following density curve shows a sampling distribution of  created by taking a...
Sampling distributions <ul><li>What effect does increasing the sample size,  n , have on the center of the sampling distri...
Sampling distributions  (answer) <ul><li>What effect does increasing the sample size,  n , have on the center of the sampl...
Sampling distributions <ul><li>What effect does increasing the sample size,  n , have on the spread of the sampling distri...
Sampling distributions  (answer) <ul><li>What effect does increasing the sample size,  n , have on the spread of the sampl...
Sampling distributions <ul><li>What effect does increasing the sample size,  n , have on the shape of the sampling distrib...
Sampling distributions  (answer) <ul><li>What effect does increasing the sample size,  n , have on the shape of the sampli...
Sampling distributions <ul><li>Which of the following would result in a decrease in the spread of the approximate sampling...
Sampling distributions  (answer) <ul><li>Which of the following would result in a decrease in the spread of the approximat...
Sampling distributions <ul><li>Time spent working out at a local gym is normally distributed with mean     = 43 minutes a...
Sampling distributions  (answer) <ul><li>Time spent working out at a local gym is normally distributed with mean     = 43...
Control charts <ul><li>On a control chart, what are on the  x  and  y  axes? </li></ul><ul><li>Time is on the  x -axis and...
Control charts  (answer) <ul><li>On a control chart, what are on the  x  and  y  axes? </li></ul><ul><li>Time is on the  x...
Control charts <ul><li>Look at the following plots.  Which show(s) a process that is out-of-control? </li></ul><ul><li>Plo...
Control charts  (answer) <ul><li>Look at the following plots.  Which show(s) a process that is out-of-control? </li></ul><...
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  1. 1. Sampling Distributions BPS chapter 11 © 2006 W.H. Freeman and Company
  2. 2. Parameters and statistics <ul><li>The average fuel tank capacity of all cars made by Ford is 14.7 gallons. This value represents a </li></ul><ul><li>Parameter because it is an average from all possible cars. </li></ul><ul><li>Parameter because it is an average from all Ford cars. </li></ul><ul><li>Statistic because it is an average from a sample of all cars. </li></ul><ul><li>Statistic because it is an average from a sample of American cars. </li></ul>
  3. 3. Parameters and statistics (answer) <ul><li>The average fuel tank capacity of all cars made by Ford is 14.7 gallons. This value represents a </li></ul><ul><li>Parameter because it is an average from all possible cars. </li></ul><ul><li>Parameter because it is an average from all Ford cars. </li></ul><ul><li>Statistic because it is an average from a sample of all cars. </li></ul><ul><li>Statistic because it is an average from a sample of American cars. </li></ul>
  4. 4. Parameters and statistics <ul><li>The fraction of all American adults who received at least one speeding ticket last year can be represented by </li></ul><ul><li>. </li></ul><ul><li>. </li></ul><ul><li>. </li></ul><ul><li>. </li></ul>
  5. 5. Parameters and statistics (answer) <ul><li>The fraction of all American adults who received at least one speeding ticket last year can be represented by </li></ul><ul><li>. </li></ul><ul><li>. </li></ul><ul><li>. </li></ul><ul><li>. </li></ul>
  6. 6. Parameters and statistics <ul><li>The mean distance traveled in a year by a sample of truck drivers can be represented by </li></ul><ul><li>. </li></ul><ul><li>. </li></ul><ul><li>. </li></ul><ul><li>. </li></ul>
  7. 7. Parameters and statistics (answer) <ul><li>The mean distance traveled in a year by a sample of truck drivers can be represented by </li></ul><ul><li>. </li></ul><ul><li>. </li></ul><ul><li>. </li></ul><ul><li>. </li></ul>
  8. 8. Sample size <ul><li>We wish to estimate the mean price,  , of all hotel rooms in Las Vegas. The Convention Bureau of Las Vegas did this in 1999 and used a sample of n = 112 rooms. In order to get a better estimate of  than the 1999 survey, we should </li></ul><ul><li>Take a larger sample because the sample mean will be closer to  . </li></ul><ul><li>Take a smaller sample since we will be less likely to get outliers. </li></ul><ul><li>Take a different sample of the same size since it does not matter what n is. </li></ul>
  9. 9. Sample size (answer) <ul><li>We wish to estimate the mean price,  , of all hotel rooms in Las Vegas. The Convention Bureau of Las Vegas did this in 1999 and used a sample of n = 112 rooms. In order to get a better estimate of  than the 1999 survey, we should </li></ul><ul><li>Take a larger sample because the sample mean will be closer to  . </li></ul><ul><li>Take a smaller sample since we will be less likely to get outliers. </li></ul><ul><li>Take a different sample of the same size since it does not matter what n is. </li></ul>
  10. 10. Law of Large Numbers <ul><li>The Law of Large Numbers says that </li></ul><ul><li>If the population is large, the estimate for  would be better than if the population was small. </li></ul><ul><li>is a good estimate for  as long as the size of the population was large. </li></ul><ul><li>If we increase our sample size, will be a better estimate for  . </li></ul><ul><li>As long as the values for x are large, our estimate for  will be good. </li></ul>
  11. 11. Law of Large Numbers (answer) <ul><li>The Law of Large Numbers says that </li></ul><ul><li>If the population is large, the estimate for  would be better than if the population was small. </li></ul><ul><li>is a good estimate for  as long as the size of the population was large. </li></ul><ul><li>If we increase our sample size, will be a better estimate for  . </li></ul><ul><li>As long as the values for x are large, our estimate for  will be good. </li></ul>
  12. 12. Sampling distribution <ul><li>If the first graph shows the population, which plot could be the sampling distribution of if all samples of size n = 50 are drawn? </li></ul><ul><li>Plot A </li></ul><ul><li>Plot B </li></ul><ul><li>Plot C </li></ul>
  13. 13. Sampling distribution (answer) <ul><li>If the first graph shows the population, which plot could be the sampling distribution of if all samples of size n = 50 are drawn? </li></ul><ul><li>Plot A </li></ul><ul><li>Plot B </li></ul><ul><li>Plot C </li></ul>
  14. 14. Sampling distribution <ul><li>Which of the following is true? </li></ul><ul><li>The shape of the sampling distribution of is always bell-shaped. </li></ul><ul><li>The shape of the sampling distribution of gets closer to the shape of the population distribution as n gets large. </li></ul><ul><li>The shape of the sampling distribution of gets approximately normal as n gets large. </li></ul><ul><li>The mean of the sampling distribution of gets closer to µ as n gets large. </li></ul>
  15. 15. Sampling distribution (answer) <ul><li>Which of the following is true? </li></ul><ul><li>The shape of the sampling distribution of is always bell-shaped. </li></ul><ul><li>The shape of the sampling distribution of gets closer to the shape of the population distribution as n gets large. </li></ul><ul><li>The shape of the sampling distribution of gets approximately normal as n gets large. </li></ul><ul><li>The mean of the sampling distribution of gets closer to µ as n gets large. </li></ul>
  16. 16. Sampling distribution <ul><li>True or false: The shape of the sampling distribution of becomes more normal the larger your sample size is. </li></ul><ul><li>True </li></ul><ul><li>False </li></ul>
  17. 17. Sampling distribution (answer) <ul><li>True or false: The shape of the sampling distribution of becomes more normal the larger your samples size is. </li></ul><ul><li>True </li></ul><ul><li>False </li></ul>
  18. 18. Sampling distribution <ul><li>True or false: The standard deviation of the sampling distribution of is always less than the standard deviation of the population when the sample size is at least 2. </li></ul><ul><li>True </li></ul><ul><li>False </li></ul>
  19. 19. Sampling distribution (answer) <ul><li>True or false: The standard deviation of the sampling distribution of is always less than the standard deviation of the population when the sample size is at least 2. </li></ul><ul><li>True </li></ul><ul><li>False </li></ul>
  20. 20. Sampling distribution <ul><li>The theoretical sampling distribution of </li></ul><ul><li>Gives the values of from all possible samples of size n from the same population. </li></ul><ul><li>Provides information about the shape, center, and spread of the values in a single sample. </li></ul><ul><li>Can only be constructed from the results of a single random sample of size n . </li></ul><ul><li>Is another name for the histogram of values in a random sample of size n . </li></ul>
  21. 21. Sampling distribution (answer) <ul><li>The theoretical sampling distribution of </li></ul><ul><li>Gives the values of from all possible samples of size n from the same population. </li></ul><ul><li>Provides information about the shape, center, and spread of the values in a single sample. </li></ul><ul><li>Can only be constructed from the results of a single random sample of size n . </li></ul><ul><li>Is another name for the histogram of values in a random sample of size n . </li></ul>
  22. 22. Standard error <ul><li>What does measure? </li></ul><ul><li>The spread of the population. </li></ul><ul><li>The spread of the ‘s. </li></ul><ul><li>Different values could be. </li></ul>
  23. 23. Standard error (answer) <ul><li>What does measure? </li></ul><ul><li>The spread of the population. </li></ul><ul><li>The spread of the ‘s. </li></ul><ul><li>Different values could be. </li></ul>
  24. 24. Sample size <ul><li>True or false: If we want the mean of all possible ‘s to equal  , then we must use a large sample size. </li></ul><ul><li>True </li></ul><ul><li>False </li></ul>
  25. 25. Sample size (answer) <ul><li>True or false: If we want the mean of all possible ‘s to equal  , then we must use a large sample size. </li></ul><ul><li>True </li></ul><ul><li>False </li></ul>
  26. 26. Sampling distributions <ul><li>The following density curve represents waiting times at a customer service counter at a national department store. The mean waiting time is 5 minutes with standard deviation 5 minutes. If we took all possible samples of size n = 100, how would you describe the sampling distribution of the ‘s? </li></ul><ul><li>Shape = right skewed, center = 5, spread = 5 </li></ul><ul><li>Shape = less right skewed, center = 5, spread = 0.5 </li></ul><ul><li>Shape = approx. normal, center = 5, spread = 5 </li></ul><ul><li>Shape = approx. normal, center = 5, spread = 0.5 </li></ul>
  27. 27. Sampling distributions (answer) <ul><li>The following density curve represents waiting times at a customer service counter at a national department store. The mean waiting time is 5 minutes with standard deviation 5 minutes. If we took all possible samples of size n = 100, how would you describe the sampling distribution of the ‘s? </li></ul><ul><li>Shape = right skewed, center = 5, spread = 5 </li></ul><ul><li>Shape = less right skewed, center = 5, spread = 0.5 </li></ul><ul><li>Shape = approx. normal, center = 5, spread = 5 </li></ul><ul><li>Shape = approx. normal, center = 5, spread = 0.5 </li></ul>
  28. 28. Central Limit Theorem <ul><li>Which is a true statement about the Central Limit Theorem? </li></ul><ul><li>We need to take repeated samples in order to estimate  . </li></ul><ul><li>It only applies to populations that are Normally distributed. </li></ul><ul><li>It says that the distribution of ‘s will have the same shape as the population. </li></ul><ul><li>It requires the condition that the sample size, n , is large and that the samples were drawn randomly. </li></ul>
  29. 29. Central Limit Theorem (answer) <ul><li>Which is a true statement about the Central Limit Theorem? </li></ul><ul><li>We need to take repeated samples in order to estimate  . </li></ul><ul><li>It only applies to populations that are Normally distributed. </li></ul><ul><li>It says that the distribution of ‘s will have the same shape as the population. </li></ul><ul><li>It requires the condition that the sample size, n , is large and that the samples were drawn randomly. </li></ul>
  30. 30. Central Limit Theorem <ul><li>True or false: The Central Limit Theorem allows us to compute probabilities on when the conditions are met. </li></ul><ul><li>True </li></ul><ul><li>False </li></ul>
  31. 31. Central Limit Theorem (answer) <ul><li>True or false: The Central Limit Theorem allows us to compute probabilities on when the conditions are met. </li></ul><ul><li>True </li></ul><ul><li>False </li></ul>
  32. 32. Sampling distributions <ul><li>The following density curve shows a sampling distribution of created by taking all possible samples of size n = 6 from a population that was very left-skewed. Which of the following would result in a decrease of the area to the left of 0.5 (denoted by the vertical line)? </li></ul><ul><li>Increasing the number of samples taken. </li></ul><ul><li>Taking a different sample. </li></ul><ul><li>Decreasing n . </li></ul><ul><li>Increasing the number of observations in each sample. </li></ul>
  33. 33. Sampling distributions (answer) <ul><li>The following density curve shows a sampling distribution of created by taking all possible samples of size n = 6 from a population that was very left-skewed. Which of the following would result in a decrease of the area to the left of 0.5 (denoted by the vertical line)? </li></ul><ul><li>Increasing the number of samples taken. </li></ul><ul><li>Taking a different sample. </li></ul><ul><li>Decreasing n . </li></ul><ul><li>Increasing the number of observations in each sample. </li></ul>
  34. 34. Sampling distributions <ul><li>What effect does increasing the sample size, n , have on the center of the sampling distribution of ? </li></ul><ul><li>The mean of the sampling distribution gets closer to the mean of the population. </li></ul><ul><li>The mean of the sampling distribution gets closer to 0. </li></ul><ul><li>The variability of the population mean is decreased. </li></ul><ul><li>It has no effect. The mean of the sampling distribution always equals the mean of the population. </li></ul>
  35. 35. Sampling distributions (answer) <ul><li>What effect does increasing the sample size, n , have on the center of the sampling distribution of ? </li></ul><ul><li>The mean of the sampling distribution gets closer to the mean of the population. </li></ul><ul><li>The mean of the sampling distribution gets closer to 0. </li></ul><ul><li>The variability of the population mean is decreased. </li></ul><ul><li>It has no effect. The mean of the sampling distribution always equals the mean of the population. </li></ul>
  36. 36. Sampling distributions <ul><li>What effect does increasing the sample size, n , have on the spread of the sampling distribution of ? </li></ul><ul><li>The spread of the sampling distribution gets closer to the spread of the population. </li></ul><ul><li>The spread of the sampling distribution gets larger. </li></ul><ul><li>The spread of the sampling distribution gets smaller. </li></ul><ul><li>It has no effect. The spread of the sampling distribution always equals the spread of the population. </li></ul>
  37. 37. Sampling distributions (answer) <ul><li>What effect does increasing the sample size, n , have on the spread of the sampling distribution of ? </li></ul><ul><li>The spread of the sampling distribution gets closer to the spread of the population. </li></ul><ul><li>The spread of the sampling distribution gets larger. </li></ul><ul><li>The spread of the sampling distribution gets smaller. </li></ul><ul><li>It has no effect. The spread of the sampling distribution always equals the spread of the population. </li></ul>
  38. 38. Sampling distributions <ul><li>What effect does increasing the sample size, n , have on the shape of the sampling distribution of ? </li></ul><ul><li>The shape of the sampling distribution gets closer to the shape of the population. </li></ul><ul><li>The shape of the sampling distribution gets more bell-shaped. </li></ul><ul><li>It has no effect. The shape of the sampling distribution always equals the shape of the population. </li></ul>
  39. 39. Sampling distributions (answer) <ul><li>What effect does increasing the sample size, n , have on the shape of the sampling distribution of ? </li></ul><ul><li>The shape of the sampling distribution gets closer to the shape of the population. </li></ul><ul><li>The shape of the sampling distribution gets more bell-shaped. </li></ul><ul><li>It has no effect. The shape of the sampling distribution always equals the shape of the population. </li></ul>
  40. 40. Sampling distributions <ul><li>Which of the following would result in a decrease in the spread of the approximate sampling distribution of ? </li></ul><ul><li>Increasing the sample size. </li></ul><ul><li>Increasing the number of samples taken. </li></ul><ul><li>Increasing the population standard deviation </li></ul><ul><li>Decreasing the value of the population mean. </li></ul>
  41. 41. Sampling distributions (answer) <ul><li>Which of the following would result in a decrease in the spread of the approximate sampling distribution of ? </li></ul><ul><li>Increasing the sample size. </li></ul><ul><li>Increasing the number of samples taken. </li></ul><ul><li>Increasing the population standard deviation </li></ul><ul><li>Decreasing the value of the population mean. </li></ul>
  42. 42. Sampling distributions <ul><li>Time spent working out at a local gym is normally distributed with mean  = 43 minutes and standard deviation  = 6 minutes. The gym took a sample of size n = 24 from its patrons. What is the distribution of ? </li></ul><ul><li>Normal with mean  = 43 minutes and standard deviation  = 6 minutes. </li></ul><ul><li>Normal with mean  = 43 minutes and standard deviation  = minutes. </li></ul><ul><li>Cannot be determined because the sample size is too small. </li></ul>
  43. 43. Sampling distributions (answer) <ul><li>Time spent working out at a local gym is normally distributed with mean  = 43 minutes and standard deviation  = 6 minutes. The gym took a sample of size n = 24 from its patrons. What is the distribution of ? </li></ul><ul><li>Normal with mean  = 43 minutes and standard deviation  = 6 minutes. </li></ul><ul><li>Normal with mean  = 43 minutes and standard deviation  = minutes. </li></ul><ul><li>Cannot be determined because the sample size is too small. </li></ul>
  44. 44. Control charts <ul><li>On a control chart, what are on the x and y axes? </li></ul><ul><li>Time is on the x -axis and the upper control limit is on the y -axis. </li></ul><ul><li>The lower control limit is on the x -axis and the upper control limit is on the y -axis. </li></ul><ul><li>Time is on the x -axis and values of the means are on the y -axis. </li></ul>
  45. 45. Control charts (answer) <ul><li>On a control chart, what are on the x and y axes? </li></ul><ul><li>Time is on the x -axis and the upper control limit is on the y -axis. </li></ul><ul><li>The lower control limit is on the x -axis and the upper control limit is on the y -axis. </li></ul><ul><li>Time is on the x -axis and values of the means are on the y -axis. </li></ul>
  46. 46. Control charts <ul><li>Look at the following plots. Which show(s) a process that is out-of-control? </li></ul><ul><li>Plot A </li></ul><ul><li>Plot B </li></ul><ul><li>Both plots </li></ul><ul><li>Neither plot </li></ul>
  47. 47. Control charts (answer) <ul><li>Look at the following plots. Which show(s) a process that is out-of-control? </li></ul><ul><li>Plot A </li></ul><ul><li>Plot B </li></ul><ul><li>Both plots </li></ul><ul><li>Neither plot </li></ul>

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