Question

Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were \(9886\) African Americans, \(2745\) Native Hawaiians, \(12,831\) Latinos, \(8,378\) Japanese Americans and \(7,650\) whites. Of the people smoking \(11\) to \(20\) cigarettes per day, there were \(6,514\) African Americans, \(3,062\) Native Hawaiians, \(4,932\) Latinos, \(10,680\) Japanese Americans, and \(9,877\) whites. Of the people smoking \(21\) to \(30\) cigarettes per day, there were \(1,671\) African Americans, \(1,419\) Native Hawaiians, \(1,406\) Latinos, \(4,715\) Japanese Americans, and \(6,062\) whites. Of the people smoking at least \(31\) cigarettes per day, there were \(759\) African Americans, \(788\) Native Hawaiians, \(800\) Latinos, \(2,305\) Japanese Americans, and \(3,970\) whites.

\(\chi^{2}\) test statistics=____

Short answer

The value of test statistics is \(10301.85\).

Step-by-step solution

Step 1. Given information

Given table-

Step 2. Calculation

The formula to calculate the test statistics is Test Statistics \(=\sum \frac{(O-E)^{2}}{E}\)

To use the formula \(=(B3-B11)*(B3-B11)/B11\) in the cell \(B18\) and drag the same formula to cell \(B21\) .After that, take the total of columns and total of rows.

Test Statistics \(=\sum \frac{(O-E)^{2}}{E}\)

\(=1523.088+169.0517+4505.49+948.6876+3155.531)\) or \(4970.562+901.76+2382.545+2046.981)\)

\(=10301.85\)

Therefore, the value of test statistics is \(10301.85\).