HW #25 More Sampling

HW #25 – More Sampling

1. (IN CLASS) Consider a population of size 4 with data given. A:6 B:8 C:6 D:15 A) Find the population mean and standard deviation. B) Draw a histogram for the population using groupings of 5.4 to 6.4, 6.4 to 7.4 etc. C) Find all samples of size 2 w/o replacement and their sample means. D) Find the mean and standard deviation of the sample means in part C.(actually do it, that is don’t use a shortcut) E) Draw a histogram for the sample means in part C using the same groupings as in part B. F) Find all samples of size 2 with replacement and their sample means. G) Find the mean and standard deviation of the sample means in part F.(actually do it, that is don’t use a shortcut) H) Draw a histogram for the sample means in part F using the same groupings as in part B.

2. (SOLUTION GIVEN) Consider a population of size 6 with data given: A:2 B:2 C:4 D:4 E:6 F:10. A) Find the population mean and standard deviation. B) Draw a histogram for the population using groupings of 1.3 to 2.3, 2.3 to 3.3 etc. C) Find all samples of size 3 w/o replacement and their sample means.(actually do it, that is don’t use a shortcut) D) Find the mean and standard deviation of the sample means in part C. E) Draw a histogram for the sample means in part C using the same groupings as in part B. F) Find all samples of size 3 with replacement and their sample means. G) Find the mean and standard deviation of the sample means in part F.(actually do it, that is don’t use a shortcut) H) Draw a histogram for the sample means in part F using the same groupings as in part B.

3. (HOMEWORK) Consider a population of size 5 with data given: A:6 B:8 C:6 D:15 E:6 A) Find the population mean and standard deviation. B) Draw a histogram for the population using groupings of 5.3 to 6.3, 6.3 to 7.3 etc. C) Find all samples of size 2 w/o replacement and their sample means. D) Find the mean and standard deviation of the sample means in part C.(actually do it, that is don’t use a shortcut). Did the mean turn out to be the same as in A? Did the standard deviation come out to be smaller than in A? E) Draw a histogram for the sample means in part C using the same groupings as in part B. F) Find all samples of size 2 with replacement and their sample means. G) Find the mean and standard deviation of the sample means in part F.(actually do it, that is don’t use a shortcut). Did the mean turn out to be the same as in A? Did the standard deviation  obey the formula  _  ? x n H) Draw a histogram for the sample means in part F using the same groupings as in part B.

4. (ALTERNATE HW) Consider a population of size 5 with data given: A:6 B:8 C:6 D:15 E:6 A) Find the population mean and standard deviation. B) Draw a histogram for the population using groupings of 5.3 to 6.3, 6.3 to 7.3 etc. C) Find all samples of size 3 w/o replacement and their sample means. D) Find the mean and standard deviation of the sample means in part C.(actually do it, that is don’t use a shortcut) E) Draw a histogram for the sample means in part C using the same groupings as in part B. F) Find all samples of size 3 with replacement and their sample means. G) Find the mean and standard deviation of the sample means in part F.(actually do it, that is don’t use a shortcut) H) Draw a histogram for the sample means in part F using the same groupings as in part B.