Transforming the data
Refer to Exercise 7.118 and the OC data for 31 females. Variables that measure concentrations such as this often have distributions that are skewed to the right. For this reason it is common to work with the logarithms of the measured values. Here are the OC values transformed with the (natural) log:
|
4.23
|
4.03
|
4.00
|
3.44
|
3.59
|
3.45
|
3.97
|
3.65
|
|
3.58
|
4.34
|
3.79
|
3.69
|
4.36
|
4.00
|
2.29
|
3.03
|
|
3.00
|
2.84
|
3.19
|
3.04
|
2.88
|
2.98
|
2.77
|
3.03
|
|
2.09
|
2.96
|
2.83
|
2.31
|
3.86
|
3.41
|
2.84
|
|
(a) Display the data with a stemplot and a boxplot. Describe the distribution.
(b) Find a 95% con?dence interval for the mean OC. Comment on the suitability of using this procedure for these data.
(c) Transform the mean and the endpoints of the con?dence interval back to the original scale, mg/ml. Compare this interval with the one you computed in Exercise 7.118.