Moore - The Basic Practice of Statistics 4/e (Homework)

James Finch

Statistics, Fall 2010

Instructor: Dr. Friendly

Current Score: 8/38

Due: Saturday, November 27, 2010 22:00 EST

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Question

Points

1	2	3	4	5
4	2/6	0/20	2/3	0/5

Total

8/38

Description

Here are some textbook questions from The Basic Practice of Statistics 4/e by Thomas A. Moore published by W. H. Freeman. Click here for a list of all of the questions coded in WebAssign.

Instructions

This demo assignment allows many submissions and allows you to try another version of the same question for practice.

1. 4/4 points All Submissions Notes Question: MBasicStat4 1.E.001.

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1	1	1	1
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4/4

Here is a small part of a data set that describes the fuel economy (in miles per gallon) of 2006 model motor vehicles.

Make and model	Vehicle type	Transmission type	Number of cylinders	City MPG	Highway MPG


.
.
.
Audi TT Roadster	Two-seater	Manual	4	20	29
Cadillac CTS	Midsize	Automatic	6	18	27
Dodge Ram 1500	Standard pickup truck	Automatic	8	14	19
Ford Focus	Compact	Automatic	4	26	32
.
.
.

2. 2/6 points All Submissions Notes Question: MBasicStat4 2.E.025.

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1	0/1	0/1	1	0/1	0/1
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2/6

The table below gives the number of medical doctors per 100,000 people in each state. The distribution is right-skewed with several high outliers.

(a) Do you expect the mean to be greater than the median, about equal to the median, or less than the median? Why?

The mean will be greater than the median because the mean is more robust and the distribution is skewed left.
The median will be greater than the mean because the mean is more robust and the distribution is skewed left.
The median will be greater than the mean because the median is more robust and the distribution is skewed right.
The mean and median will be about the same because both are robust and the distribution is skewed right.
The mean will be greater than the median because the median is more robust and the distribution is skewed right.
The mean and median will be about the same because they are both a measure of center and the distribution is symmetric.
Your answer is correct.

Calculate x and M and verify your expectation. (Give answers to 1 decimal place.)

x =	Enter a number. 2
M =	Enter a number. 3

(b) The District of Columbia, at 683 doctors per 100,000 residents, is a high outlier. If you remove D.C. because it is a city rather than a state, do you expect x or M to change more? Why?

Outliers have a greater effect on the mean, so removing D.C. should change x more than M. Outliers have a greater effect on the median, so removing D.C. should change M more than x. Outliers have no effect on either, so removing D.C. should not change the value of x or M.

Your answer is correct.

Omitting D.C., calculate both measures for the 50 states and verify your expectation. (Give answers to 1 decimal place.)

x =	Enter a number. 5
M =	Enter a number. 6

3. –/20 points Notes Question: MBasicStat4 3.E.029.

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1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1	0/1
0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50	0/50

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0/20

Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:

114
108
111

100
130
103

104
120
74

89
132
112

102
111
107

91
128
103

114
118
98

114
119
96

103
86
112

105
72
112

(a) We expect IQ scores to be approximately Normal. Make a stemplot to check that there are no major departures from Normality. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)

Stems	Leaves
7	Answer is not case sensitive. 1
7	Answer is not case sensitive. 2
8	Answer is not case sensitive. 3
8	Answer is not case sensitive. 4
9	Answer is not case sensitive. 5
9	Answer is not case sensitive. 6
10	Answer is not case sensitive. 7
10	Answer is not case sensitive. 8
11	Answer is not case sensitive. 9
11	Answer is not case sensitive. 10
12	Answer is not case sensitive. 11
12	Answer is not case sensitive. 12
13	Answer is not case sensitive. 13
13	Answer is not case sensitive. 14

(b) Nonetheless, proportions calculated from a Normal distribution are not always very accurate for small numbers of observations. Find the mean x and standard deviation s for these IQ scores. (Give answers to 2 decimal places.)

x	= Enter a number. 15
s	= Enter a number. 16

What proportions of the scores are within one standard deviation and within two standard deviations of the mean? (Give answers to 1 decimal place.)

within one standard deviation	= Enter a number. 17%
within two standard deviations	= Enter a number. 18%

What would these proportions be in an exactly Normal distribution? (Round answers to an integer.)

within one standard deviation	= Enter an exact number. 19%
within two standard deviations	= Enter an exact number. 20%

4. 2/3 points All Submissions Notes Question: MBasicStat4 4.E.024.

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1	0/1	1
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2/3

A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man each woman dates. Here are the data (heights in inches).

Women (x)	65	64	65	64	71	64
Men (y)	73	68	70	68	71	64

(a) Make a scatterplot of these data. (Do this on paper. Your instructor may ask you to turn in this work.) Based on the scatterplot, do you expect the correlation to be positive or negative? Near ± 1 or not?

Negative, but not close to 1. Positive, but not close to 1. Positive and close to 1. Negative and close to 1.

Your answer is correct.

(b) Find the correlation r between the heights of the men and women. (Give answer to 3 decimal places.)
r =

Do the data show that taller women tend to date taller men?
Your answer is correct.

5. –/5 points Notes Question: MBasicStat4 5.E.027.

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0/1	0/1	0/1	0/1	0/1
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0/5

The Sanchez household is about to install solar panels to reduce the cost of heating their house. In order to know how much the solar panels help, they record their consumption of natural gas before the panels are installed. Outside temperature is recorded in degree-days, a common measure of demand for heating. A day's degree-days are the number of degrees its average temperature falls below 65°F. Gas used is recorded in hundreds of cubic feet. The data below is for 16 consecutive months.

Month	Nov.	Dec.	Jan.	Feb.	Mar.	Apr.	May	June
Degree-days per day	23	53	43	32	28	12	3	0
Gas used per day	6.5	11.3	8.7	8	5.4	4.0	1.6	1.3
Month	July	Aug.	Sept.	Oct.	Nov.	Dec.	Jan.	Feb.
Degree-days per day	0	2	6	10	25	35	52	31
Gas used per day	1.2	1.3	2.3	3.2	6.2	7.3	11.0	6.8

(a) Mr. Sanchez asks, "If a month averages 18 degree-days per day (that's 47°F), how much gas will we use?" Use your calculator or software to find the least-squares regression line. (Use 3 decimal places.)
yhat

= + x

Answer his question. (Use 2 decimal places.)
hundred cubic feet is the predicted gas usage

(b) Make a scatterplot for these data. (Do this on paper. Your instructor may ask you to turn in this work.)

Calculate r ². (Use 1 decimal place.)
r ² = %

Based on your scatterplot and r ², do you expect your prediction from the regression line to be quite accurate? Why? (Select all that apply.)

This should be a reasonably accurate prediction. The scatterplot showed very little scatter about the line. This would not be a reasonably accurate prediction. The correlation is quite low. The correlation is quite high. The scatterplot showed very a lot of scatter about the line.

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Moore - The Basic Practice of Statistics 4/e (Homework)

Current Score: 8/38