2. Suppose that for the process of 1, the qq-normal plot of the empirical distribution X30e suggests it is close enough to a normal distribution to use a t-approximation. The sample mean is ¯x = 1.127 and its standard deviation is s = 0.988. The estimate of the t29 distribution is given by 1, 000 resamples of size 30 from the data, and have the following values for t29e:

.5% 1% 2.5% 5% 10% 90% 95% 97.5% 99% 99.5%

t 29e −0.052 −0.047 −0.040 −0.034 −0.026 0.022 0.028 0.036 0.045 0.049

Use the t confidence interval method along with this estimated t29 table to make a C = 99% confidence interval for μP . This is known as a studentized confidence interval.

3. Suppose that for the process of 1, the null hypothesis is H0 : μP = 1.0 versus the alternative hypothesis H1 : μP > 1.0, and you find that ¯x = 1.480. Use the empirical distribution given in the percentile table of 1 to do a level = 5% test of H0, and report your conclusions. Whatever that conclusion, assume that H0 is true to report the p-value of ¯x.

4. Explain why the bootstrap procedure is not useful for analyzing the distribution of estimates of the minimum and maximum values of a distribution. Hint: What are differences between distribution of the extreme values of 1, 000 resamples (~se)i, i = 1, . . . , 1000 of a given ~s, and the distribution the extreme values of 1, 000 samples {~si}, i = 1, . . . , 1000.

Thank you for your help.