Use a ?² Test to Test the Claim That in the Given

question 30

Essay

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent
-An observed frequency distribution is as follows: $\begin{array}{l|lll}\text { Number of successes } & 0 & 1 & 2 \\\hline \text { Frequency } & 47 & 98 & 55\end{array}$
i) Assuming a binomial distribution with $n = 2$ and $p = 1 / 2$ , use the binomial formula to find the probability corresponding to each category of the table.
ii) Using the probabilities found in part (i), find the expected frequency for each category.
iii) Use a $0.05$ level of significance to test the claim that the observed frequencies fit a binomial distribution for w 2 and $p = 1 / 2$ =

---

Definitions:

Joints

The locations where two or more bones meet, allowing for movement and flexibility of the skeletal system.

Kinesthetic Receptors

Sensory receptors located in muscles, joints, and tendons that detect bodily movement, position, and tension, contributing to the sense of proprioception.

Body Position

The arrangement or posture of the body, which can significantly affect health, comfort, and physical performance.

Movements

Actions or activities of changing position or place, or the potential for change in the physical position of the body or of objects.