Chapter 8

None of the above (there’s no sample being selected here; the entire population is being surveyed)

Stratified random sample (the strata are the different majors)

Simple random sample

 

 

Southeast

Just over 10%

Outlying Areas and Rocky Mtns.

Twenty-four

The longest commutes are 60, 50, and 36 miles; the shortest are 4, 6, and 7 miles.

4, 6, 7, 10, 10, 10, 12, 12, 12, 14, 15, 18, 18, 20, 25, 25, 25, 30, 30, 35, 35, 36, 50, 60

Answers may vary based on bin choices. Here’s the result for bins of width 2,500:

The data are strongly right-skewed.

Top ten teams by wins:

There are two modes: 89 and 104, each of which appears three times.

2

136

82.5

2

12.556

$\frac{62}{33}=1.879$

Modes: 72, 84, 93, 97
Median: 82.5
Mean: 80.967 (rounded to three decimal places)

Mode or median

Median or mean

Median or mean

67

$\mathrm{\$<!--\; \$\; -->}74,514-<!--\; -\; -->\mathrm{\$<!--\; \$\; -->}480=\mathrm{\$<!--\; \$\; -->}74,034$

$s=\sqrt{752.5}\approx <!--\; \approx \; -->27.432$

$13,333.77.

15

70th percentile

1026

1318

82.7th

99.2nd

$3,120

$26,465.20

32.3rd

98.5th

The red (leftmost) distribution has mean 11, the blue (middle) has mean 13, and the yellow (rightmost) has mean 14.

6

Mean: 150; standard deviation: 20

99.7%

95%

68%

65 and 75

26 and 54

110 and 290

47.5%

15.85%

81.5%

$-1.8$
$1.6$
$-0.6$

–44
30
6

80th

9th

97th

3.9

6.3

2.9

1.29

94.5th

An LSAT score of 161 is better

72

6

93^rd

Using NORM.INV: 1092.8

Using PERCENTILE: 1085

Income

Either; neither one seems to directly influence the other (they’re both influenced by the student’s academic ability)

GPA

$$

1. No curved pattern
2. Strong negative relationship, $r\approx <!--\; \approx \; -->-<!--\; -\; -->0.9$

$$

1. Curved pattern

$$

1. No curved pattern
2. No apparent relationship, $r\approx <!--\; \approx \; -->0$

$$

1. No curved pattern
2. Weak positive relationship, $r\approx <!--\; \approx \; -->0.6$

 

1. $r=-<!--\; -\; -->0.91$
2. Not appropriate
3. $r=-<!--\; -\; -->0.01$
4. $r=0.62$

$y=0.75\left(\frac{20}{5}\right)(x-<!--\; -\; -->100)+200=3x-<!--\; -\; -->100$

$y=1.8x+16.9$

$y=0.174x+14.5$

26.68

Predicted: 28; actual: 18. The Phillies were caught around 10 fewer times than expected.

Every 10 additional steal attempts will result in getting caught about 1.7 times on average.

$y=0.5481x+0.1055$, where x is the proportion of made field goals and y is the proportion of made three-point field goals

0.347

Predicted: 0.340; actual: 0.368. The Aces made about 2.8% more of their three-point shots than expected.

An increase of 1% in made field goal attempts will result in an expected increase of 0.55% in made three-point field goal attempts.

Randomization is being used; cluster random sample.

No randomization is being used.

Randomization is being used; stratified random sample.

Mode: 112

Median: 113

Mean: 112.64

3

3

$\frac{107}{32}\approx <!--\; \approx \; -->3.344$

156

147

147.2

Mode: not useful; every value appears only once

Median: 0.322

Mean: 0.3612

Mode: not useful; every value appears only once

Median: $42,952

Mean: $42924.78

Mode: $13,380
Median: $11,207
Mean: $15,476.79

Since the data are right skewed, the mean will be bigger than the mean. Thus, the workers would rather use the median, while the management will prefer the mean.

9

$\sqrt{10.5}\approx <!--\; \approx \; -->3.240$

$168-<!--\; -\; -->127=41$

11.306

Range: $0.6617-<!--\; -\; -->0.1404=0.5213$

Standard deviation: 0.170

Range: $\mathrm{\$<!--\; \$\; -->}43,394-<!--\; -\; -->42,218=\mathrm{\$<!--\; \$\; -->}1,176$

Standard deviation: $398.37

18

14

80th

60th

71.7

101.2

70.25

51.7th

79.3rd

13.8th

95%

34%

84th

0.583

71.2

72nd

115.38

27th

23.2

1300 on the SAT

$\mathrm{\mu <!--\; \mu \; -->}=60$; $\mathrm{\sigma <!--\; \sigma \; -->}=\frac{1}{2}\sqrt{120}\approx <!--\; \approx \; -->5.477$

96.6th

57

PERCENTILE gives 20.86; NORM.INV gives 21.11.

PERCENTILE gives 11.82; NORM.INV gives 11.68.

PERCENTRANK gives 92.6th; NORM.DIST gives 91.9th.

PERCENTRANK gives 77th; NORM.DIST gives 79.2nd.

 

1. Yes

 

1. No
2. Weak positive relationship; $r\approx <!--\; \approx \; -->0.5$

0.96

$y=2900x–478$

$7,475

Less than expected by $1,495.68

For every $1,000 increase in out-of-state tuition, we expect average monthly salary to increase by $161.