**Chi-Square Test for Independence: Education and Health Levels**The table below represents the relationship between the level of health and the level of education for a random sample of 1,641 residents.| Education | Excellent | Good | Fair | Poor ||--------------------------|-----------|------|------|------|| Not a H.S. graduate | 64 | 148 | 94 | 124 || H.S. graduate | 54 | 125 | 111 | 104 || Some college | 74 | 154 | 95 | 106 || Bachelor Degree or higher| 64 | 135 | 98 | 91 |**Hypotheses:**1. **$H_1$:** Level of education and health are dependent.2. **Options:** - $H_0: p_1 = p_2 = p_3$ - $H_1:$ At least one of the proportions are not equal. OR - $H_0: \mu_1 = E_1 \text{ and } \mu_2 = E_2 \text{ and } \mu_3 = E_3 \text{ and } \mu_4 = E_4$ - $H_1:$ At least one mean is different from what is expected.**Task:**Calculate the test statistic:\[\chi^2_0 = ?\](Round to three decimal places as needed.)Enter your answer in the answer box and then click Check Answer.

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Description: **Chi-Square Test for Independence: Education and Health Levels**The table below represents the relationship between the level of health and the level of education for a random sample of 1,641 residents.| Education | Excellent | Good

Given Information: Data represents the level of health and the level of education for a random sample of 1641 residents. Education Excellent Good Fair Poor Total Not a H.S graduate 64 148 94 124 430 H.S graduate 54 125 111 104 394 Some college 74 154 95 106 429 Bachelor degree or Higher 64 135 98 91 388 Total 256 562 398 425 1641 Null Hypothesis: Level of education and health are independent. Alternative Hypothesis: Level of education and health are dependent. Chi square test statistic is given by the formula: χ2=∑iOi-Ei2Ei where, Oi : Observed frequencies Ei : Expected frequencies Expected frequencies are calculated using the formula: E=Corresponding row total×Corresponding column total/Grand Total Education Excellent Good Fair Poor Total Not a H.S graduate 430×2561641=67.0810 430×5621641=147.2639 104.2901 111.3650 430 H.S graduate 394×2561641=61.4650 134.9348 95.5588 102.0414 394 Some college 66.9250 146.9214 104.0475 111.1060 429 Bachelor degree or Higher 60.5289 132.8800 94.1036 100.4875 388 Total 256 562 398 425 1641 Calculation of the test statistic: χ2=∑iOi-Ei2Ei=64-67.0810267.0810+148-147.26392147.2639+......91-100.48752100.4875=0.1415+0.0037+1.0153+1.4335+....≈10.1651 Thus, the value of the test statistic is 10.165

Math

Statistics

Education Good Fair he following data represent the level of health and the level of education for a random sample of 1641 residents. Complete parts (a) Not a H.S. graduate and (b) below. Excellent 64 148 94 H.S. graduate Some college Bachelor Degree or higher 54 125 111 74 154 95 64 135 98 H: Level of educalion and health are dependent. OB. H P, = P, =P3 H,: At least one of the proportions are not equal. O C. Ho: H =E, and u = E, and p =E, and p =E, H: At least one mean is different from what is expected. Calculate the test statistic. (Round to three decimal places as needed.)

Education Good Fair he following data represent the level of health and the level of education for a random sample of 1641 residents. Complete parts (a) Not a H.S. graduate and (b) below. Excellent 64 148 94 H.S. graduate Some college Bachelor Degree or higher 54 125 111 74 154 95 64 135 98 H: Level of educalion and health are dependent. OB. H P, = P, =P3 H,: At least one of the proportions are not equal. O C. Ho: H =E, and u = E, and p =E, and p =E, H: At least one mean is different from what is expected. Calculate the test statistic. (Round to three decimal places as needed.)

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**Chi-Square Test for Independence: Education and Health Levels**

The table below represents the relationship between the level of health and the level of education for a random sample of 1,641 residents.

| Education | Excellent | Good | Fair | Poor |
|--------------------------|-----------|------|------|------|
| Not a H.S. graduate | 64 | 148 | 94 | 124 |
| H.S. graduate | 54 | 125 | 111 | 104 |
| Some college | 74 | 154 | 95 | 106 |
| Bachelor Degree or higher| 64 | 135 | 98 | 91 |

**Hypotheses:**

1. **$H_1$:** Level of education and health are dependent.

2. **Options:**

- $H_0: p_1 = p_2 = p_3$
- $H_1:$ At least one of the proportions are not equal.

OR

- $H_0: \mu_1 = E_1 \text{ and } \mu_2 = E_2 \text{ and } \mu_3 = E_3 \text{ and } \mu_4 = E_4$
- $H_1:$ At least one mean is different from what is expected.

**Task:**
Calculate the test statistic:

\[
\chi^2_0 = ?
\]

(Round to three decimal places as needed.)

Enter your answer in the answer box and then click Check Answer.

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