Compute the ?-value of the chi-square statistic, ?2, using software. Give your answer in decimal form with precision to four decimal places.
Compute the ?-value of the chi-square statistic, ?2, using software. Give your answer in decimal form with precision to four decimal places.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Compute the ?-value of the chi-square statistic, ?2, using software. Give your answer in decimal form with precision to four decimal places.
![According to Benford's Law, also known as the first-digit law, many sets of data contain numbers that have a distribution
of leading digits as outlined in the table. The test proportions represent the hypothesized distribution of the leading digits
according to Benford's Law.
The table displays a summary of observed counts of leading digits for a simple random sample of 2011 diabetes
incidences for 300 U.S. counties. Perform a chi-square goodness-of-fit test using this data.
Leading digit Observed count Test proportion Expected count Contribution to chi-square
1
94
0.301
90.3
0.152
2
56
0.176
52.8
0.194
3
31
0.125
37.5
1.127
4
27
0.097
29.1
0.152
5
27
0.079
23.7
0.459
22
0.067
20.1
0.18
7
18
0.058
17.4
0.021
8
12
0.051
15.3
0.712
9
13
0.046
13.8
0.046
Chi-square statistic: 3.042](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F060fdeba-f711-4f79-8cf5-45a731455e17%2Ff62ed8de-7276-4a40-99ba-502e64b5cad9%2Ftxz0b8_processed.png&w=3840&q=75)
Transcribed Image Text:According to Benford's Law, also known as the first-digit law, many sets of data contain numbers that have a distribution
of leading digits as outlined in the table. The test proportions represent the hypothesized distribution of the leading digits
according to Benford's Law.
The table displays a summary of observed counts of leading digits for a simple random sample of 2011 diabetes
incidences for 300 U.S. counties. Perform a chi-square goodness-of-fit test using this data.
Leading digit Observed count Test proportion Expected count Contribution to chi-square
1
94
0.301
90.3
0.152
2
56
0.176
52.8
0.194
3
31
0.125
37.5
1.127
4
27
0.097
29.1
0.152
5
27
0.079
23.7
0.459
22
0.067
20.1
0.18
7
18
0.058
17.4
0.021
8
12
0.051
15.3
0.712
9
13
0.046
13.8
0.046
Chi-square statistic: 3.042
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Follow-up Questions
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Follow-up Question
Compute the ?-value of the chi-square statistic, ?^2. Give your answer in decimal form with precision to four decimal places.
Solution
Follow-up Question
Compute the P- value of the chi-square statistic, X^2, using software. You may find software manuals helpful. Give your answer in decimal form with precision to four decimal places.
Solution
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