Question

The following data represent crime rates per 1000 population for a random sample of 46 Denver neighborhoods.† 63.2 36.3 26.2 53.2 65.3 32.0 65.0 66.3 68.9 35.2 25.1 32.5 54.0 42.4 77.5 123.2 66.3 92.7 56.9 77.1 27.5 69.2 73.8 71.5 58.5 67.2 78.6 33.2 74.9 45.1 132.1 104.7 63.2 59.6 75.7 39.2 69.9 87.5 56.0 154.2 85.5 77.5 84.7 24.2 37.5 41.1 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.) x = crimes per 1000 people s = crimes per 1000 people (b) Let us say the preceding data are representative of the population crime rates in Denver neighborhoods. Compute an 80% confidence interval for μ, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.) lower limit crimes per 1000 people upper limit crimes per 1000 people (c) Suppose you are advising the police department about police patrol assignments. One neighborhood has a crime rate of 57 crimes per 1000 population. Do you think that this rate is below the average population crime rate and that fewer patrols could safely be assigned to this neighborhood? Use the confidence interval to justify your answer. Yes. The confidence interval indicates that this crime rate is below the average population crime rate. Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate. No. The confidence interval indicates that this crime rate is below the average population crime rate. No. The confidence interval indicates that this crime rate does not differ from the average population crime rate. (d) Another neighborhood has a crime rate of 77 crimes per 1000 population. Does this crime rate seem to be higher than the population average? Would you recommend assigning more patrols to this neighborhood? Use the confidence interval to justify your answer. Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate. Yes. The confidence interval indicates that this crime rate is higher than the average population crime rate. No. The confidence interval indicates that this crime rate is higher than the average population crime rate. No. The confidence interval indicates that this crime rate does not differ from the average population crime rate. (e) Compute a 95% confidence interval for μ, the population mean crime rate for all Denver neighborhoods. (Round your answers to one decimal place.) lower limit crimes per 1000 people upper limit crimes per 1000 people (f) Suppose you are advising the police department about police patrol assignments. One neighborhood has a crime rate of 57 crimes per 1000 population. Do you think that this rate is below the average population crime rate and that fewer patrols could safely be assigned to this neighborhood? Use the confidence interval to justify your answer. Yes. The confidence interval indicates that this crime rate is below the average population crime rate. Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate. No. The confidence interval indicates that this crime rate is below the average population crime rate. No. The confidence interval indicates that this crime rate does not differ from the average population crime rate. (g) Another neighborhood has a crime rate of 77 crimes per 1000 population. Does this crime rate seem to be higher than the population average? Would you recommend assigning more patrols to this neighborhood? Use the confidence interval to justify your answer. Yes. The confidence interval indicates that this crime rate does not differ from the average population crime rate. Yes. The confidence interval indicates that this crime rate is higher than the average population crime rate. No. The confidence interval indicates that this crime rate is higher than the average population crime rate. No. The confidence interval indicates that this crime rate does not differ from the average population crime rate. (h) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem. Yes. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal. Yes. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal. No. According to the central limit theorem, when n ≥ 30, the x distribution is approximately normal. No. According to the central limit theorem, when n ≤ 30, the x distribution is approximately normal.

Answer #1

The following data represent crime rates per 1000 population for
a random sample of 46 Denver neighborhoods.†
63.2
36.3
26.2
53.2
65.3
32.0
65.0
66.3
68.9
35.2
25.1
32.5
54.0
42.4
77.5
123.2
66.3
92.7
56.9
77.1
27.5
69.2
73.8
71.5
58.5
67.2
78.6
33.2
74.9
45.1
132.1
104.7
63.2
59.6
75.7
39.2
69.9
87.5
56.0
154.2
85.5
77.5
84.7
24.2
37.5
41.1
(a) Use a calculator with mean and sample standard deviation
keys to find the sample mean x...

Let x be a random variable representing percentage
change in neighborhood population in the past few years, and let
y be a random variable representing crime rate (crimes per
1000 population). A random sample of six Denver neighborhoods gave
the following information.
x
30
3
11
17
7
6
y
170
35
132
127
69
53
Σx = 74; Σy = 586; Σx2 =
1,404; Σy2 = 71,248; Σxy = 9,617
(a) Find x, y, b, and the equation of...

A random sample of n1 = 10 regions in New
England gave the following violent crime rates (per million
population).
x1: New England Crime
Rate
3.5
3.9
4.0
4.1
3.3
4.1
1.8
4.8
2.9
3.1
Another random sample of n2 = 12 regions in
the Rocky Mountain states gave the following violent crime rates
(per million population).
x2: Rocky Mountain Crime
Rate
3.7
4.1
4.7
5.3
3.3
4.8
3.5
2.4
3.1
3.5
5.2
2.8
Assume that the crime rate distribution...

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Use a calculator with mean...

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Use a calculator with mean...

The home run percentage is the number of home runs per 100 times
at bat. A random sample of 43 professional baseball players gave
the following data for home run percentages.
1.6
2.4
1.2
6.6
2.3
0.0
1.8
2.5
6.5
1.8
2.7
2.0
1.9
1.3
2.7
1.7
1.3
2.1
2.8
1.4
3.8
2.1
3.4
1.3
1.5
2.9
2.6
0.0
4.1
2.9
1.9
2.4
0.0
1.8
3.1
3.8
3.2
1.6
4.2
0.0
1.2
1.8
2.4
(a) Use a calculator with mean...

At wind speeds above 1000 centimeters per second (cm/sec),
significant sand-moving events begin to occur. Wind speeds below
1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move
sand to new locations. The cyclic nature of wind and moving sand
determines the shape and location of large dunes. At a test site,
the prevailing direction of the wind did not change noticeably.
However, the velocity did change. Sixty-five wind speed readings
gave an average velocity of x = 1075...

At wind speeds above 1000 centimeters per second (cm/sec),
significant sand-moving events begin to occur. Wind speeds below
1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move
sand to new locations. The cyclic nature of wind and moving sand
determines the shape and location of large dunes. At a test site,
the prevailing direction of the wind did not change noticeably.
However, the velocity did change. Sixty-two wind speed readings
gave an average velocity of x = 1075...

A random sample of n1 = 10 regions in New
England gave the following violent crime rates (per million
population).
x1: New England Crime
Rate
3.5
3.7
4.2
4.1
3.3
4.1
1.8
4.8
2.9
3.1
Another random sample of n2 = 12 regions in
the Rocky Mountain states gave the following violent crime rates
(per million population).
x2: Rocky Mountain Crime
Rate
3.9
4.1
4.5
5.1
3.3
4.8
3.5
2.4
3.1
3.5
5.2
2.8
Assume that the crime rate distribution...

A random sample of n1 = 10 regions in New England gave the
following violent crime rates (per million population).
x1: New England Crime Rate 3.3 3.9 4.2 4.1 3.3 4.1 1.8 4.8 2.9
3.1
Another random sample of n2 = 12 regions in the Rocky Mountain
states gave the following violent crime rates (per million
population).
x2: Rocky Mountain Crime Rate 3.5 4.3 4.5 5.3 3.3 4.8 3.5 2.4
3.1 3.5 5.2 2.8
Assume that the crime rate distribution...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 19 minutes ago

asked 22 minutes ago

asked 28 minutes ago

asked 44 minutes ago

asked 51 minutes ago

asked 55 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago