Question

Collecting Averages of Groups of Five Repeat steps one through five (of the section titled Collect the Data) with one exception. Instead of recording the change of 30 classmates, record the average change of 30 groups of five. 1. Randomly survey 30groups of fiveclassmates. 2. Record the values of the average of their change.
Chapter 7 | The Central Limit Theorem 419
__________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ Table 7.3
3. Construct a histogram. Scale the axes using the same scaling you used for the section titled Collect the Data. Sketch the graph using a ruler and a pencil.
Figure 7.12
4. Calculate the following (n= 5; surveying five people at a time): a. x ¯ = _______ b. s= _______ 5. Draw a smooth curve through tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve. Discussion Questions 1. Why did the shape of the distribution of the data change, as n changed? Use one to two complete sentences to explain what happened. 2. In the section titled Collect the Data, what was the approximate distribution of the data? X ~ _____(_____,_____) 3. In the section titled Collecting Averages of Groups of Five, what was the approximate distribution of the averages? X ¯ ~ _____(_____,_____) 4. In one to two complete sentences, explain any differences in your answers to the previous two questions.

Answer 1

SOLUTION :-

3)

Random selection of 30 pairs of data

Classmate 1	Classmate 2	Average
0.35	0.5	0.425
0.33	0.2	0.265
0.25	0	0.125
0.25	0.75	0.5
0.1	0.25	0.175
0.33	0.25	0.29
0	0.1	0.05
0.5	0.35	0.425
0.85	0.98	0.915
0.1	0.1	0.1
0.99	0	0.495
0.9	0.2	0.55
0.75	0.99	0.87
0	0.3	0.15
0.35	0.35	0.35
0.3	0.75	0.525
0.35	0.5	0.425
0.9	0.75	0.825
0.1	0.5	0.3
0.75	0.99	0.87
0.75	0.33	0.54
0.5	0.5	0.5
0.75	0.1	0.425
0.9	0.3	0.6
0.5	0.9	0.7
0.1	0.5	0.3
0.85	0.5	0.675
0.1	0.3	0.2
0.2	0.75	0.475
0.5	0.33	0.415

Histogram for the Average values

Select the bins as 0, 0.1, 0.2, till 1.

0	Frequency	Cumulative %
0.1	2	6.90%
0.2	4	20.69%
0.3	4	34.48%
0.4	1	37.93%
0.5	8	65.52%
0.6	4	79.31%
0.7	2	86.21%
0.8	0	86.21%
0.9	3	96.55%
1	1	100.00%
More	0	100.00%

4)

For this particular set of values, we get