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.
(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.
(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?