STATISTICS 101 - Homework 1
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Homework is due by 5:00 PM on the due date at your course instructor’s office. You can always hand in your homework at the end of lecture on Friday.
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You may talk with others about the homework problems but please write your solutions up independently.
•
Please answer homework questions in complete sentences. Make sure to assignment together.
the pages of your
Homework with out the correct lab section will marked as late.
• You normally will have an opportunity to get help on homework during lab.
Jan. 14 -Jan. 18 Section 1.1
Jan. 21 -Jan. 25 Section 1.2
1. Read pages 1-20 of the text and do problems 1.2, 1.8, 1.12 and 1.22.
Read pages 28-32 of the text and do problem 1.28.
2. The birth weight (grams) for each of 44 babies born at a Brisbane, Australia hospital are summarized in the frequency table below.
Number
Birth Weight (g),
X of babies
1500
≤ X <
1750 1
1750
≤ X <
2000
2000
≤ X <
2250
2250
≤ X <
2500
2500
≤ X <
2750
0
3
1
2
2750
≤ X <
3000
3000
≤ X <
3250
3250
≤ X <
3500
3500
≤ X <
3750
3750
≤ X <
4000
4000
≤ X <
4250
4250
≤ X <
4500
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.
(d) Which would be greater the sample mean or the sample median? Explain briefly.
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
10.4
8.8
9.7
7.8
9.9
11.7
8.0
9.3
9.0
8.5
8.6
8.2
8.9
10.1
9.4
9.2
7.9
9.5
10.9
7.8
8.3
8.2
9.2
9.1
8.4
9.6
11.1
7.9
8.5
8.7
7.8
10.5
8.5
9.0
8.5
11.5
8.0
7.9
8.3
8.7
10.0
9.4
9.0
9.2
10.7
10.2
9.6
9.3
9.7
8.7
8.2
8.9
8.6
9.5
9.4
8.8
8.3
9.5
9.0
8.4
9.1
10.1
7.8
8.1
8.8
8.0
9.2
8.4
7.8
8.3
10.7
7.9
8.5
9.2
8.7
10.2
7.9
9.8
8.3
9.0
9.6
8.9
8.6
9.9
10.6
8.6
9.4
8.8
8.2
10.5
9.7
9.1
8.0
9.1
10.0
8.7
9.8
8.5
8.9
9.1
8.4
8.1
9.5
8.7
9.3
10.3
10.8
8.1
10.1
9.6
8.3
8.0
9.8
9.0
8.9
8.1
9.7
8.4
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?
(e) Compute the median gain for the 120 amplifiers. Interpret this median value within the context of the problem.
(f) Will the mean gain for the 120 amplifiers be less than, approximately equal to, or greater than the median? Explain your reasoning briefly.
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.
Heart Attack No Heart Attack
270 236 210 142 234 360 288 196 232 200 242 212 162
280 272 160 220 224 310 288 206 178 184 198 200 164
226 242 186 266 276 280 244 160 182 182 198 182 176
206 318 294 282 282 278 236 182 238 198 188 230 218
166 204 182 178 186 170
(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?