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

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 $p = 1 / 2$ =