Statistics 101 – Homework 1
Due Friday, September 2, 2005
Homework is due on the due date at the end of the lecture.
Reading:
August 25 – August 29
August 29 – September 2
Chapters 3 & 4
Chapter 5
Assignment:
1. Students in a statistics class at Penn State University were asked “With whom is it
easiest to make friends?” The choices were “The opposite sex,” “The same sex,”
and “It makes no difference.” Students also indicated their gender (male or
female). The data are summarized below. Source: Utts and Heckard (2004),
Mind on Statistics, Belmont, CA: Brooks/Cole, pages 529-530.
With whom is it easiest to make friends?
Same Sex
Opposite Sex
No Difference
16
58
63
13
15
40
29
73
103
Female
Male
Total
Total
137
68
205
a) Answer the questions, Who? What? When? Where? Why? How? for these data.
b) Create an appropriately labeled bar chart with a percentage scale. What does the
bar chart indicate about how easy it is to make friends?
c) Find row percentages. What do these percentages indicate about the difference
between females and males in terms of how easy it is to make friends?
d) Extra Credit: Use JMP to make a segmented bar chart (mosaic plot) that displays
the percentages in c). Turn in the JMP output.
2. The low temperatures (degrees Fahrenheit) for a sample of 52 cities in the United
States are given below.
44
21
11
24
38
11
27
38
35
22
24
31
31
27
14
24
42
45
27
49
15
12
34
18
22
25
31
7
26
23
0
32
30
21
26
33
45
2
21
19
37
24
28
9
22
8
33
13
19
13
24
14
a) Make a stem-and-leaf display of the low temperatures.
b) Describe the distribution of the low temperatures. Make sure to mention shape,
center, spread and any outliers in the distribution.
c) Using the summary ∑ yi = 1271 , find the sample mean low temperature.
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3. The birth weights (grams) for each of 44 babies born at a Brisbane, Australia
hospital are summarized in the frequency table below.
Birth Weight (grams), X
1500 ≤ X < 1750
1750 ≤ X < 2000
2000 ≤ X < 2250
2250 ≤ X < 2500
2500 ≤ X < 2750
2750 ≤ X < 3000
3000 ≤ X < 3250
3250 ≤ X < 3500
3500 ≤ X < 3750
3750 ≤ X < 4000
4000 ≤ X < 4250
4250 ≤ X < 4500
Number of babies
1
0
3
1
2
2
5
13
11
5
1
0
a) Construct an appropriately labeled histogram from the frequency table above.
b) What percentage of babies weigh less than 2500 grams (about 5.5 pounds)? What
percentage of babies weigh greater than or equal to 4000 grams (about 8.8
pounds)?
c) Describe the distribution of birth weights. Be sure to discuss shape, center, spread
and any outliers.
4. JMP Assignment: A telecommunications equipment manufacturer was getting
complaints about low volume on long distance calls. Amplifiers are used to boost
the signal at various points in the long distance lines. The boosting ability of the
amplifiers is called “gain.” Amplifiers are designed to have a gain of 10 decibels
(dB). This means that a 1 dB input signal would be boosted to a 10 dB output
signal. A sample of 120 amplifiers is tested for gain. The data are located on the
main course webpage as Amplifier Gain. Source: “The Tools of Quality Part IV:
Histograms,” Quality Progress, September 1990, Vol. XXIII, No. 9, pages 75-78.
Follow the instructions in the JMP Guide to download the data from the web,
open the data in JMP, and obtain a histogram, stem-and-leaf display and
descriptive statistics for the gain. Print the JMP output and turn it in with your
assignment. Use the output to answer the following questions.
a) Answer the questions, Who? What? When? Where? Why? How? for these data.
b) Describe the distribution of amplifier gain. Make sure to mention the shape,
center, spread and any outliers.
c) What percentage of amplifiers have a gain less than 10 dB?
d) What is the sample median amplifier gain? What is the sample mean amplifier
gain?
e) Comment on the relationship between the sample median and sample mean and
how this relationship is consistent with your description of the shape of the
distribution.
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