Investigation 6: More on “Tipping Point” connectors (due Wed, Jan 25)
You may work with one other person on this assignment, handing in one report with both names. Word-processed reports are preferred to hand-written ones. Please copy/paste relevant, well-labeled Minitab output into a Word file as appropriate.
Recall that based on the idea presented in Malcolm Gladwell’s book The Tipping Point, I asked each of you
to determine how many people you know with last names appearing on a list of
250 names taken randomly from the
6 7 8
10 10 10
10 11 11
12 13 14
14
15 15 15
15 16 16
16 17 18
18 18 19
19
19 20 20
20 21
21 21 21
22 23 23
23 24
24 25 26
27 27 27
27 27 28
29 31 33
33
33 33 33
33 35 35
36 36 36
36 36 36
37
37 39 40
40 40 41
44 45
45 46 47
48 48
49 49 49
50 50 53
54 62 65
65 67 70
72
82 85 85
86 98 107
127 139
These data appear in C1 of the Minitab worksheet GladwellConnectorData.mtw. The mean is 36.10 people, and the standard deviation is 25.25 people. Let mu represent the population mean number of people known from this list among all Cal Poly students.
(a) Are 36.10 and 25.25 parameters or statistics? Explain, and also indicate what symbols we use to represent them.
(b) Determine a 95% confidence interval for mu.
(c) Interpret this interval, including an interpretation of what the phrase “95% confident” means.
(d) Determine a 90% confidence interval for mu. Comment on how it compares to the 95% confidence interval. [Mention both the midpoints and widths of the intervals.] Explain why this makes sense.
(e) Comment on whether the technical conditions required for the validity of the t-interval are satisfied here.
(f) Determine what proportion of the sample values fall within the 90% confidence interval. Is this proportion close to 90%? Should it be? Explain.