Chapter 25, Problem 12E

(a)

To determine

To discuss why the box plots show outliers for each sites yet the histogram shows none.

Explanation of Solution

From the previous question we get the summary statistics for wind speeds at two sites near each other both being considered as locations for an electricity generating wind turbine. And the two displays of these data are shown in the question. The box plots are given for the two sites and the histogram is also given to show the difference in readings. Thus, the box plots show outliers for each sites yet the histogram shows none because the outliers are very windy days, but it was windy at both sites so the difference in wind speeds isn't unusual.

(b)

To determine

To explain which of the summaries would you use to select between these sites and why.

Answer to Problem 12E

The histogram and summaries of the differences are more appropriate to select between these sites.

Explanation of Solution

From the previous question we get the summary statistics for wind speeds at two sites near each other both being considered as locations for an electricity generating wind turbine. And the two displays of these data are shown in the question. The box plots are given for the two sites and the histogram is also given to show the difference in readings. Thus, the histogram and summaries of the differences are more appropriate to select between these sites because they're paired observations and all we care about is which site is windier.

(c)

To determine

To discuss the assumptions and conditions for paired t -inference for these data.

Answer to Problem 12E

All the conditions are not met.

Explanation of Solution

From the previous question we get the summary statistics for wind speeds at two sites near each other both being considered as locations for an electricity generating wind turbine. And the two displays of these data are shown in the question. The box plots are given for the two sites and the histogram is also given to show the difference in readings. Thus, the histogram and summaries of the differences are more appropriate to select between these sites. So, the assumptions and conditions for paired t -inference for these data are as follows: The wind measurements at the same site are paired. They may not be independent until the times are six hours apart. This isn't random but the sample is large enough to represent the wind speeds at these sites. The histograms are uni-modal, symmetric, and bell-shaped. Thus, all the conditions are not met.