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 || 6 | 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: 3.042This table helps to assess how well the observed data fits the expected distribution proposed by Benford's Law through a chi-square test. Each row presents the leading digit, its observed and expected counts, the test proportion, and the contribution to the total chi-square statistic.

Given data, Digit Observed Test proportion 1 94 0.301 2 56 0.176 3 31 0.125 4 27 0.097 5 27 0.079 6 22 0.067 7 18 0.058 8 12 0.051 9 13 0.046 Step-by-step procedure to perform test using MINITAB software: Choose Stat > Tables > Chi-Square Goodness-of-fit(one variable) Select ‘Observed’ in Observed counts. Select Digits under category names. Select Test proportion in Proportions specified by historical counts under Click The output is given as follows: From the above output, The test statistic value is 3.042. P-value is 0.9316. Decision rule: If p-value ≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis. Conclusion: Assume Level of significance as 0.1 Here, p-value (0.9316) is greater than the level of significance (0.1). Therefore, fail to reject the null hypothesis.

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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 |
| 6 | 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

This table helps to assess how well the observed data fits the expected distribution proposed by Benford's Law through a chi-square test. Each row presents the leading digit, its observed and expected counts, the test proportion, and the contribution to the total chi-square statistic.

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