Question

This data is also on the BbLearn site. You can copy and paste it Distance (inches) for both from the site into Minitab. cold rubber bands and In preparation for your Topic 1 Extended Problem report, do the following: rubber bands stored at room temperature 1. For the cold rubber bands, construct a frequency histogram and a cumulative frequency histogram. 2. For the room temperature rubber bands, construct a frequency histogram and a cumulative frequency histogram. 3. For the room temperature rubber bands, construct an ordered stem and leaf plot. 4. Find the mean, median, variance, and standard deviation for the cold rubber bands. Room Temp Cold 144 217 164 214 151 200 156 193 157 180 132 159 148 5. Find the mean, median, variance, and standard deviation for the room temperature rubber bands. 202 149 203 6. Find the z-score for the cold band that flew 156 inches. 152 179 7. Find the z-score for the room temperature band that flew band that flew 180 inches. 146 180 148 184 8. Find the 5-number summary for the cold bands and then find the 5-number summary for the room temperature bands. Draw side by side box plots. 165 191 168 209 154 220 168 227 Write a report that includes all of the data, statistics, and graphs from above and answers the following questions. Use complete sentences-imagine this is a report for your boss. Your graphs should be produced using Minitab and then pasted into your report. 174 180 175 199 151 208 152 215 153 219 156 168 What kind of data was this? . 202 Based on your graphs and plots, does the data appear to be skewed or symmetrical? Do you see anything that looks like an outlier? 208 Was this study an experiment? Can you see a difference in dispersion between room temperature and cold rubber bands? What does this say in the real world? Use z-scores to compare how far each of the cold bands that flew 156 inches and the room temperature band that flew 180 inches are from each of their respective Do you think the temperature makes a difference? Explain. Any other interesting comments? means.

Answer 1

1.

Cold						Class boundary	Frequency	Cumulative frequency
144		Maximum=	208			132-148	5	5
164		Minimum=	132			148-164	11	16
151		n=	23			164-180	5	21
156		Then we see that 2^4<23<2^5				180-196	0	21
157		so no. of classes=k=5				196-212	2	23
132		Range=	76
148		Width=	16
149
152
146
148
165
168
154
168
174
175
151
152
153
156
202
208

Frequency Histogram 12 10 2 196-212 132-148 148-164 164-180 180-196 Class boundary Cumulative Frequency Histogram 20 15 10 0 180-196 132-148 148-164 164-180 196-212 Class boundary Cumulative Frequency Frequency 25

2.

Room Temp						Class boundary	Frequency	Cumulative frequency
217		Maximum=	227			159-173	2	2
214		Minimum=	159			173-187	5	7
200		n=	21			187-201	4	11
193		Then we see that 2^4<21<2^5				201-215	6	17
180		so no. of classes=k=5				215-229	4	21
159		Range=	68
202		Width=	14
203
179
180
184
191
209
220
227
180
199
208
215
219
168

Cumulative Frequency Histogram 7 6 1 0 215-229 159-173 173-187 187-201 201-215 class boundary Cumulative Frequency Histogram 20 10 0 173-187 187-201 159-173 201-215 215-229 class boundary Cumulative Frequency Cumulative Frequency D un 25

3.

Stem-and-Leaf Display: Room Temp

Stem-and-leaf of Room Temp N = 21
Leaf Unit = 1.0

1 15 9
2 16 8
3 17 9
7 18 0004
10 19 139
(5) 20 02389
6 21 4579
2 22 07

4.

Descriptive Statistics: Cold

Variable Mean StDev Variance Median
Cold 159.70 17.47 305.31 154.00

5.

Descriptive Statistics: Room Temp

Variable Mean StDev Variance Median
Room Temp 197.48 18.65 347.86 200.00

6.

z-score for the cold band that flew 156 inches=(156-159.70)/17.47=-0.2118

7.

z-score for the room temperature band that flew 180 inches=(180-197.48)/18.65=-0.9373

8.

Descriptive Statistics: Cold, Room Temp

Variable Minimum Q1 Median Q3 Maximum
Cold 132.00 149.00 154.00 168.00 208.00
Room Temp 159.00 180.00 200.00 214.50 227.00

Boxplot of Cold, Room Temp 240 220 200 180 160 140 120 Room Temp Cold Data