Suppose I measure some treatment response on a set of 10 mice from strain A, and receive the following data:
84 | 106 | 99 | 101 | 100 |
99 | 127 | 105 | 101 | 108 |
Note that n=10, the sample mean is 103 and the sample SD is 10.67.
Suppose I measure the same sort of treatment response on a set of 5 mice from strain B, and receive the following data:
56 | 62 | 67 | 81 | 69 |
Note that m=5, the sample mean is 67 and the sample SD is 9.30.
Calculate a 95% confidence interval for the difference in the average treatment responses of strains A and B.
Suppose I measure some treatment response on a set of 6 mice from a particular strain, and receive the following data:
107 | 101 | 93 | 94 | 96 | 114 |
Note that the sample mean is 100.83 and the sample SD is 8.28.
Imagine that the data are independent draws from some normal distribution.
Calculate a 95% confidence interval for the population mean.
Calculate a 95% confidence interval for the population SD. (Note that the the 2.5 and 97.5 percentiles of the chi-square distribution with 5 degrees of freedom are 0.8312 and 12.83, respectively.
Consider data on the treatment response of 12 mice from strain A and 9 mice from strain B.
Strain A: | 132 | 72 | 102 | 115 | 59 | 103 | sample mean = | 96.58 | ||
86 | 159 | 60 | 94 | 80 | 97 | sample SD = | 29.09 | |||
Strain B: | 101 | 96 | 93 | 106 | 81 | 77 | sample mean = | 92.33 | ||
106 | 97 | 74 | sample SD = | 12.17 |
Assume that the measurements from strain A are independent draws from a normal distribution with mean muA and SD sigmaA, and that the the measurements from strain B are independent draws from a normal distribution with mean muB and SD sigmaB.
Calculate an approximate 95% confidence interval for the difference between the strain means, allowing for the possibility that the two strains have different SDs.
Last modified: Wed Feb 22 09:43:29 EST 2006 |