Find the value of the $\chi ^ { 2 }$ test statistic for a hypothesis test of independence. Round your answer to 3 decimal places.
-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. $$\begin{array} { l | c c c }
\text { Blood Pressure } & \text { Low } & \text { Moderate } & \text { High } \
\hline \text { Walkers } & 35 & 62 & 25 \
\text { Non-walkers } & 21 & 65 & 28
\end{array}$$
A)9.210
B)0.176
C)3.473
D)3.743

Question

Find the value of the $\chi ^ { 2 }$ test statistic for a hypothesis test of independence. Round your answer to 3 decimal places.
-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. $$\begin{array} { l | c c c } 
\text { Blood Pressure } & \text { Low } & \text { Moderate } & \text { High } \
\hline \text { Walkers } & 35 & 62 & 25 \
\text { Non-walkers } & 21 & 65 & 28
\end{array}$$
A)9.210
B)0.176
C)3.473
D)3.743

Quizplus · Accepted Answer

To calculate the $\chi^2$ test statistic for independence, we first need to calculate the expected frequencies for each cell in the table, assuming that walking and blood pressure levels are independent. The formula for expected frequency is $(\text{row total} \times \text{column total}) / \text{total sample size}$. Then, we use the formula $\chi^2 = \sum \frac{(O - E)^2}{E}$, where $O$ is the observed frequency and $E$ is the expected frequency.1. Calculate row and column totals:- Walkers: $35 + 62 + 25 = 122$- Non-walkers: $21 + 65 + 28 = 114$- Low: $35 + 21 = 56$- Moderate: $62 + 65 = 127$- High: $25 + 28 = 53$- Total: $236$2. Calculate expected frequencies for each cell:- Expected frequency for Walkers with Low BP: $(122 \times 56) / 236$- And so on for each cell...3. Calculate $\chi^2$ value using the formula.After performing these calculations, the $\chi^2$ test statistic is found to be approximately 3.473, which matches choice C. This involves detailed calculations for each cell, which are not fully shown here due to space constraints but follow the outlined steps.

Find the Value of The χ2\chi ^ { 2 }χ2 Test Statistic for a Hypothesis Test of Independence

Find the Value of The $\chi ^ { 2 }$ Test Statistic for a Hypothesis Test of Independence