In February 2012, a bill was introduced into the Ohio State Senate that would ou
ID: 3376286 • Letter: I
Question
In February 2012, a bill was introduced into the Ohio State Senate that would outlaw smoking in vehicles if young children are present. That same month a poll was conducted by Quinnipiac University and asked randomly selected Ohio voters if they thought this bill was a good idea or a bad idea. Of the 1,421 respondents, 55% said it was a good idea. We can use this sample proportion to investigate whether more than half of all Ohio voters in February 2012 thought that this bill was a good ideaDescribe how we could conduct a simulation to decide whether a simple random sample from this population could produce a sample proportion like 0.55 if, in fact, only 50% of the population supports ban on smoking in cars when young children are present.
Each trial represents _____________________________________________
Number of trials =
Probability of success =
Explanation / Answer
Solution
Since the theoretical probability is ½, simulation can be done by tossing an unbiased coin a number of times till proportion of times heads turns up is 55%.
Alternatively, single-digit random numbers can be generated and counting the number of digits greater than 4 (i.e., 0, 1, 2, 3, 4), which again has a theoretical probability of ½. This process can be continued till the proportion of odd digits is 0.55.
DONE
[Going beyond, to make the point clear, the latter procedure is demonstrated below:
Lines 10580–10594, columns 21–40, from
RAND Corporation - RAND's A Million Random Digits
73735 45963 78134 63873 02965 58303 90708 20025 98859 23851
27965 62394 33665 63570 64775 78428 81665 26440 20422 05720
15838 47174 76866 14330 89793 34378 08730 56522 78155 22466
81978 57323 16381 66207 11698 99314 75002 80827 53867 37797
Codes used in the following Simulation Table
SN: Simulation #; RN: Random Number;
#less5: Cumulative Number of digits less than 5;
prop(<5): Cumulative Proportion of digits less than 5.
SN
RN
#less5
prop(<5)
1
7
1
1
2
3
1
0.5
3
7
2
0.6666667
4
3
2
0.5
5
5
3
0.6
6
4
3
0.5
7
5
4
0.5714286
8
9
5
0.625
9
6
6
0.6666667
10
3
6
0.6
11
7
7
0.6363636
12
8
8
0.6666667
13
1
8
0.6153846
14
3
8
0.5714286
15
4
8
0.5333333
16
6
9
0.5625
17
3
9
0.5294118
18
8
10
0.5555556
19
7
11
0.5789474
20
3
11
0.55
Lines 10580–10594, columns 21–40, from
RAND Corporation - RAND's A Million Random Digits
73735 45963 78134 63873 02965 58303 90708 20025 98859 23851
27965 62394 33665 63570 64775 78428 81665 26440 20422 05720
15838 47174 76866 14330 89793 34378 08730 56522 78155 22466
81978 57323 16381 66207 11698 99314 75002 80827 53867 37797