Math / Data & Statistics

QuestionProvide an appropriate response. A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and the results are given below. Find the critical value $x_{0}^{2}$ to test the claim that walking and low, moderate, and high blood pressure are not related. Use $\alpha=0.01$ . \begin{tabular}{l|ccc} Blood Pressure & Low & Moderate & High \\ \hline Walkers & 35 & 62 & 25 \\ Non-walkers & 21 & 65 & 28 \end{tabular} 9.348 9.210 6.251 0.584

Studdy Solution

STEP 1

1. The problem involves a chi-square test of independence.
2. The significance level $\alpha$ is 0.01.
3. The degrees of freedom for the test can be calculated based on the contingency table.

STEP 2

1. Determine the degrees of freedom.
2. Find the critical value $x_{0}^{2}$ using the chi-square distribution table.

STEP 3

Calculate the degrees of freedom for the chi-square test. The formula for degrees of freedom in a contingency table is:
$(df) = (r - 1) \times (c - 1)$
where $r$ is the number of rows and $c$ is the number of columns.
In this case, there are 2 rows (Walkers, Non-walkers) and 3 columns (Low, Moderate, High), so:
$(df) = (2 - 1) \times (3 - 1) = 1 \times 2 = 2$

STEP 4

Using the chi-square distribution table, find the critical value for $\alpha = 0.01$ with $df = 2$ .
The critical value $x_{0}^{2}$ for $\alpha = 0.01$ and $df = 2$ is approximately:
$9.210$
The critical value $x_{0}^{2}$ is:
$\boxed{9.210}$

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