The homogeneity of the chloride level in a water sample from a lake was tested by analyzing portions drawn from the top and from near the bottom of the lake, with the following results in ppm Cl: Top Bottom 26.30 26.22 26.43 26.32 26.28 26.20 26.19 26.11 26.49 26.42 (a) Apply the t-test at the 95% confidence level to determine if the chloride level from the top of the lake is different from that at the bottom. At 95% confidence t crit = , and t = . Since t (>,<,=) we conclude that (a,no) significant difference exists at the 95% confidence level. (b) Now use the paired t-test and determine whether there is a significant difference between the top and bottom values at the 95% confidence level. At 95% confidence t crit = and t = . Since t (>,<,=) we conclude that (a,no) significant difference exists at the 95% confidence level. (c) Why is a different conclusion drawn from using the paired t-test than from just pooling the data and using the normal t-test for differences in means? The large sample to sample variability causes s top and s bottom to be large and masks the differences between the samples taken from the top and the bottom. Because there are reduced degrees of freedom with the paired t-test, the significant difference detected is artificial. There are multiple outliers in the Top data that artificially skew the mean, and therefore the t-crit value.
The homogeneity of the chloride level in a water sample from a lake was tested by analyzing portions drawn from the top and from near the bottom of the lake, with the following results in ppm Cl: Top Bottom 26.30 26.22 26.43 26.32 26.28 26.20 26.19 26.11 26.49 26.42 (a) Apply the t-test at the 95% confidence level to determine if the chloride level from the top of the lake is different from that at the bottom. At 95% confidence t crit = , and t = . Since t (>,<,=) we conclude that (a,no) significant difference exists at the 95% confidence level. (b) Now use the paired t-test and determine whether there is a significant difference between the top and bottom values at the 95% confidence level. At 95% confidence t crit = and t = . Since t (>,<,=) we conclude that (a,no) significant difference exists at the 95% confidence level. (c) Why is a different conclusion drawn from using the paired t-test than from just pooling the data and using the normal t-test for differences in means? The large sample to sample variability causes s top and s bottom to be large and masks the differences between the samples taken from the top and the bottom. Because there are reduced degrees of freedom with the paired t-test, the significant difference detected is artificial. There are multiple outliers in the Top data that artificially skew the mean, and therefore the t-crit value.
Basic Clinical Laboratory Techniques 6E
6th Edition
ISBN:9781133893943
Author:ESTRIDGE
Publisher:ESTRIDGE
Chapter1: The Clinical Laboratory
Section1.9: Quality Assessment
Problem 1.1CT
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The homogeneity of the chloride level in a water sample from a lake was tested by analyzing portions drawn from the top and from near the bottom of the lake, with the following results in ppm Cl:
| Top | Bottom |
| 26.30 | 26.22 |
| 26.43 | 26.32 |
| 26.28 | 26.20 |
| 26.19 | 26.11 |
| 26.49 | 26.42 |
(a) Apply the t-test at the 95% confidence level to determine if the chloride level from the top of the lake is different from that at the bottom.
At 95% confidence t crit = , and t = . Since t (>,<,=) we conclude that (a,no) significant difference exists at the 95% confidence level.
(b) Now use the paired t-test and determine whether there is a significant difference between the top and bottom values at the 95% confidence level.
At 95% confidence t crit = and t = . Since t (>,<,=) we conclude that (a,no) significant difference exists at the 95% confidence level.
(c) Why is a different conclusion drawn from using the paired t-test than from just pooling the data and using the normal t-test for differences in means?
The large sample to sample variability causes s top and s bottom to be large and masks the differences between the samples taken from the top and the bottom.
Because there are reduced degrees of freedom with the paired t-test, the significant difference detected is artificial.
There are multiple outliers in the Top data that artificially skew the mean, and therefore the t-crit value.
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