Introduction to the Practice of Statistics

Introduction to the Practice of Statistics

Sixth Edition

Moore, McCabe

Section 1.1 Homework Answers

1.21 An aging population. The population of the United States is aging, though less rapidly than in other developed countries. Here is a stemplot of the percents of residents aged 65 and over in the 50 states, according to the 2000 census. The stems are whole percents and the leaves are tenths of a percent.

a) There are two outliers: Alaska has the lowest percent of older residents, and Florida has the highest. What are the percents for those two states?

17.6% for Florida and 5.7% for Alaska.

b) Ignoring Alaska and Florida, describe the shape, center, and spread of this distribution.

The distribution is fairly symmetric, with the center being around 12.8% and the spread about 7.1%.

1.22 Split the stems. Make another stemplot of the percent of residents aged 65 and over in the states other than Alaska and Florida by splitting stems 8 to 15 in the previous exercise.

8
8 / 5
9
9 / 6 / 7 / 8
10
10 / 6
11 / 0 / 2 / 2 / 3 / 3
11 / 6 / 7 / 7
12 / 0 / 0 / 1 / 1 / 1 / 1 / 3 / 4 / 4 / 5
12 / 7 / 8 / 9
13 / 0 / 0 / 0 / 1 / 2 / 2 / 3 / 3 / 3 / 4
13 / 5 / 5 / 6 / 8
14 / 0 / 3 / 4
14 / 5 / 7 / 9
15 / 3
15 / 6

Stems represent whole percents.
1.23 Diabetes and glucose. People with diabetes must monitor and control their blood glucose level. The goal is to maintain “fasting plasma glucose” between about 90 and 130 milligrams per deciliter (mg/dl). Here are the fasting plasma glucose levels for 18 diabetics enrolled in a diabetes control class, five months after the end of the class.

Make a stemplot of these data and describe the main features of the distribution. (You will want to trim and also split stems.) Are there outliers? How well is the group as a whole achieving the goal for controlling glucose levels?

141 / 158 / 112 / 153 / 134 / 95 / 96 / 78 / 148
172 / 200 / 271 / 103 / 172 / 359 / 145 / 147 / 255
0
0 / 8
1 / 0 / 0 / 0 / 1 / 3 / 4
1 / 5 / 5 / 5 / 5 / 6 / 7 / 7
2 / 0
2 / 6 / 7
3
3 / 6

The stem represents 100 of milligrams.

The stemplot was created using rounding.

The possible outlier from the data seems to be the 359 mg/dl glucose measurement, and 271 mg/dl is a possible outlier as well. The shape of the distribution is slightly right skewed. The data suggests that less than half of the people are achieving the prescribed goal of 90 mg/dl to 130 mg/dl.

1.39 Oil Wells. How much oil the wells in a given field will ultimately produce is key information in deciding whether to drill more wells. Here are the estimated total amounts of oil recovered from 64 wells in the Devonian Richmond Dolomite area of the Michigan basin, in thousands of barrels.

tens
0 / 2 / 2 / 3 / 7
1 / 0 / 0 / 2 / 2 / 2 / 4 / 4 / 7 / 8 / 8
2 / 0 / 1 / 4 / 6 / 8 / 9
3 / 0 / 1 / 2 / 2 / 3 / 4 / 4 / 5 / 6 / 7 / 7 / 7 / 8
4 / 2 / 3 / 4 / 4 / 6 / 7 / 9
5 / 0 / 1 / 3 / 4 / 6 / 7 / 8
6 / 1 / 3 / 4 / 5 / 9
7 / 9
8 / 1 / 2
9 / 2 / 7
10 / 3
11 / 8
12
13
14
15 / 6
16
17
18
19 / 9
20 / 4

The graph below was created using the trimming method.

Oil
2 / 21.71 / 37.9 / 61.4
2.5 / 24.9 / 38.6 / 63.1
3 / 26.9 / 42.7 / 64.9
7.1 / 28.3 / 43.4 / 65.6
10.1 / 29.1 / 44.5 / 69.5
10.3 / 30.5 / 44.9 / 69.8
12 / 31.4 / 46.4 / 79.5
12.1 / 32.5 / 47.6 / 81.1
12.9 / 32.9 / 49.4 / 82.2
14.7 / 33.7 / 50.4 / 92.2
14.8 / 34.6 / 51.9 / 97.7
17.6 / 34.6 / 53.2 / 103.1
18 / 35.1 / 54.2 / 118.2
18.5 / 36.6 / 56.4 / 156.5
20.1 / 37 / 57.4 / 196
21.3 / 37.7 / 58.8 / 204.9

This is a right skewed distribution, with a spread of 202 thousands of barrels.

The center is approximately 38 thousands of barrels.

1.41 Time spent studying. Do women study more than men? We asked the students in a large first-year college class how many minutes they studied on a typical weeknight. Here are the responses for random samples of 30 women and 30 men from the class.

a) Study the data. Why are you not surprised that most responses are multiples of 10 minutes? We eliminated one student who claimed to study 30,000 minutes per night. Are there any other responses you consider suspicious?

(a) When asked the question of how many minutes one studies a night, most people would try to be accurate to the half-hour only, which is a multiple of 10. The rest of the values seem reasonable; there is the female student that studies 6 hours a night, while possible, it seems excessive that this is typical. At the same time it is one student and it can be considered an outlier (an unusual value).

b) Make a back-to-back stemplot of these data. Report the approximate midpoints of both groups. Does is appear that women study more than men.

Female / Male
0 / 0 / 3 / 3 / 3 / 3
9 / 6 / 0 / 5 / 6 / 6 / 6 / 8 / 9 / 9 / 9
2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 1 / 0 / 2 / 2 / 2 / 2 / 2 / 2 / 2
8 / 8 / 8 / 8 / 8 / 8 / 8 / 8 / 8 / 8 / 7 / 5 / 5 / 5 / 1 / 5 / 5 / 8
4 / 4 / 4 / 0 / 2 / 0 / 0 / 3 / 4 / 4
2
3 / 0
6 / 3

It seems on average women do tend to study longer per night than men. The peak for the men is lower in the number of minutes than for the women.