STATISTICS 101 L - Homework 1
Due Friday, January 23, 2004
• Homework is due by 4:00 PM on the due date at 327 Snedecor. You can always hand in your homework
at the end of lecture on Friday.
• You may talk with others about the homework problems but please write up your solutions independently.
• Please answer homework questions in complete sentences. Make sure to
assignment together.
staple the pages of your
• You normally will have an opportunity to get help on homework during lab.
Reading:
Jan. 12
Jan. 21
- Jan. 16
- Jan. 23
Section 1.1
Section 1.2
Assignment:
1. Read pages 1-22 of the text and do problems 1.8, 1.10, 1.18 and 1.20.
2. The birth weight (grams) for each of 44 babies born at a Brisbane, Australia hospital are summarized
in the frequency table below.
Birth
1500
1750
2000
2250
2500
2750
3000
3250
3500
3750
4000
4250
Weight (g), X
≤ X < 1750
≤ X < 2000
≤ X < 2250
≤ X < 2500
≤ X < 2750
≤ X < 3000
≤ X < 3250
≤ X < 3500
≤ X < 3750
≤ X < 4000
≤ X < 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 have birth weights less than 2500 grams (about 5.5 pounds)? What
percentage of birth weights are greater than or equal to 4000 grams (about 8.8 pounds)?
(c) Describe the distribution of birth weights. Be sure to discuss the center, the spread and the shape
of the distribution.
3. A telecommunications equipment manufacturer was getting complaints about low volume on longdistance calls. Amplifiers are used to boost the signal at various points in the long-distance lines. The
boosting ability of the amplifiers, referred to as “gain”, was the likeliest potential cause. 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. The team assigned to investigate the problem took 120 amplifiers and tested
them for gain. The data is given in “The Tools of Quality Part IV: Histograms” (Quality Progress,
September 1990, Vol. XXIII, No. 9, pp. 75-78) and appears below.
8.1
8.2
9.1
11.5
9.3
8.4
7.9
9.9
8.7
8.1
10.4
8.9
8.4
8.0
9.7
9.1
8.5
10.6
9.8
10.1
8.8
10.1
9.6
7.9
8.7
10.1
9.2
8.6
8.5
9.6
9.7
9.4
11.1
8.3
8.2
7.8
8.7
9.4
8.9
8.3
7.8
9.2
7.9
8.7
8.9
8.1
10.2
8.8
9.1
8.0
9.9
7.9
8.5
10.0
8.6
8.8
7.9
8.2
8.4
9.8
11.7
9.5
8.7
9.4
9.5
8.0
9.8
10.5
8.1
9.0
8.0
10.9
7.8
9.0
9.4
9.2
8.3
9.7
9.5
8.9
9.3
7.8
10.5
9.2
8.8
8.4
9.0
9.1
8.7
8.1
9.0
8.3
8.5
10.7
8.3
7.8
9.6
8.0
9.3
9.7
8.5
8.2
9.0
10.2
9.5
8.3
8.9
9.1
10.3
8.4
8.6
9.2
8.5
9.6
9.0
10.7
8.6
10.0
10.8
8.6
(a) Construct a stem-and-leaf display. Using a split stem will be helpful.
(b) Below is a histogram using classes 7.5 ≤ Y < 8.0, 8.0 ≤ Y < 8.5, 8.5 ≤ Y < 9.0, etc.
From the histogram, describe the distribution of gains. Be sure to comment on the center, spread
and shape.
(c) What percentage of amplifiers have a gain less than 8.0 dB?
(d) What percentage of amplifiers have a gain greater than or equal to 11 dB?
4. A study was conducted regarding blood cholesterol levels of 28 heart-attack patients and 30 people
who had not had a heart attack. Below are the data.
270
280
226
206
236
272
242
318
Heart Attack
210 142 234
160 220 224
186 266 276
294 282 282
360
310
280
278
288
288
244
236
196
206
160
182
166
No Heart Attack
232 200 242 212
178 184 198 200
182 182 198 182
238 198 188 230
204 182 178 186
162
164
176
218
170
(a) Construct a back-to-back stem plot and compare the two groups in terms of cholesterol levels.
(b) Compute the mean cholesterol level for each group. Which group has the higher average cholesterol
level?