1. One classic application of correlation involves the association between the temperature and the number of times a cricket chirps in one minute. Listed below are the number of chirps in 1 minute and the corresponding temperatures in ?F. Is there sufficient evidence to conclude that there is a linear correlation between the number of chirps in 1 minute and the temperature?
|
Chirps in 1 min
|
882
|
1188
|
864
|
1104
|
864
|
1200
|
1032
|
960
|
900
|
|
Temperature (?F)
|
69.7
|
93.3
|
76.3
|
84.3
|
76.3
|
88.6
|
82.6
|
71.6
|
79.6
|
2. For the data in #1, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5, Section 10-3.
Find the best predicted temperature at a time when a cricket chirps 3000 times in 1 minute. What is wrong with this predicted value?
3. According to Benford's Law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. Test for goodness-of-fit with Benford's Law.
|
Leading Digit
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
Benford's Law: Distribution of Leading Digits
|
30.1%
|
17.6%
|
12.5%
|
9.7%
|
7.9%
|
6.7%
|
5.8%
|
5.1%
|
4.6%
|
Here are the observed frequencies of the leading digits from the amounts on checks written by Mr. K:
68, 40, 18, 19, 8, 20, 6, 9, 12. (Those observed frequencies correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.) Using a 0.05 significance level, test the claim that these leading digits are from a population of leading digits that conform to Benford's Law. Do Mr. K's check amounts appear to be legitimate?
4. The table below shows results since 2006 of challenged referee calls in the U.S. Open. Use a 0.05 significance level to test the claim that gender of the tennis player is independent of whether the call is overturned.
|
Was the Challenge to the Call Successful?
|
|
Yes
|
No
|
|
Men
|
411
|
981
|
|
Women
|
210
|
529
|