Page 130 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

Exercises 109

3.14 Consider the CT G dataset. Compute the 95% and 99% confidence intervals of the
standard deviation of the ASTV variable. Are the confidence interval limits equally
away from the sample mean? Why?

3.15 Consider the computation of the confidence interval for the standard deviation
performed in Example 3.6. How many cases should one have available in order to
obtain confidence interval limits deviating less than 5% of the point estimate?

3.16 In order to represent the area values of the cork defects in a convenient measurement
unit, the ART values of the Cork Stoppers dataset have been multiplied by 5 and
stored into variable ART5. Using the point estimates and 95% confidence intervals of
the mean and the standard deviation of ART, determine the respective statistics for
ART5.

3.17 Consider the ART, ARM and N variables of the Cork Stoppers’ dataset. Since
ARM = ART/N, why isn’t the point estimate of the ART mean equal to the ratio of the
point estimates of the ART and N means? (See properties of the mean in A.6.1.)

3.18 Redo Example 3.8 for the classes C = “calm vigilance” and D = “active vigilance” of
the CTG dataset.

3.19 Using the bootstrap technique compute confidence intervals at 95% level of the mean
and standard deviation for the ART data of Example 3.11.

3.20 Determine histograms of the bootstrap distribution of the median of the river Cávado
flow rate (see Flow Rate dataset). Explain why it is unreasonable to set confidence
intervals based on these histograms.

3.21 Using the bootstrap technique compute confidence intervals at 95% level of the mean
and the two-tail 5% trimmed mean for the BRISA data of the Stock Exc hange
dataset. Compare both results.

3.22 Using the bootstrap technique compute confidence intervals at 95% level of the
Pearson correlation between variables CaO and MgO of the Clays’ dataset.