Preventable chronic diseases are increasing rapidly in some regions, particularl

Question

Preventable chronic diseases are increasing rapidly in some regions, particularly diabetes. Shown below is a contingency table showing cross classification of educational attainment and diabetic state for a random sample of 1478 people in a region (Hs is high school). At the 1% significance level, do the data provide sufficient evidence to conclude that an association exists between educational level and diabetic state for the region? Less than HS HS grad Some college College grad Total 35 366 401 23 377 400 34 346 380 24 273 297 116 1362 1478 abetes diabetes Total What are the null and alternative hypotheses? A. Ho. The variable educational level is dependent upon diabetic state. H.: The variable diabetic state is dependent upon educational level Ho. The two variables, educational level and diabetic state, are associated H.: The two variables, educational level and dabetic state, are not associated. O B. C. Ho: The two variables, educational level and dabetic state, are not associated. H.: The two variables, educational level and dabetic state, are associated The test statistic is (Round to three decimal places as needed.)

Explanation / Answer

Here question (A) Is correctly Done. Null and Alternative Hypothesis are correcty definded. Now we wil do Chi-square testing for alpha = 0.01

Here the observed table is

Here Expected Values are calculated i.e.

For Diabetes/ Less than HS = Total Diabetes * Toal Less than HS people/ Total number of people = 401 * 116/ 1478 = 31.47

For Non diabetes/Less than HS = Total non diabetes * Toal Less than HS people/ Total number of people =401 * 1362/ 1478 = 369.53

SImilarly, we will calculate expected table

NOw we will calculate X2

which is equal to X2 = (oi -Ei)2/Ei

The chi - square table for each ingredient is given below

Here X2 = 3.521

Lesss than HS HS Grad Some College College Grad Total Diabetes 35 23 34 24 116 No diabetes 366 377 346 273 1362 Total 401 400 380 297 1478

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