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

question 10

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: $$\begin{array} { l | l l l } \text { Number of successes } & 0 & 1 & 2 \\\hline \text { Frequency } & 41 & 93 & 66\end{array}$$ 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 which n = 2 and p = 1/2.

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Definitions:

Thrifty Genotype

A hypothesis that suggests certain populations have a genetic predisposition to efficiently store fat to survive famines, which can lead to obesity in environments with plentiful food.

Food Scarcity

A situation where the availability of food is insufficient to meet the needs of the population, leading to hunger and malnutrition.

Dairying People

Groups or cultures that specialize in the production and processing of milk and milk products for consumption.

Obese

A medical condition characterized by excess body fat that presents significant health risks, including diabetes, heart disease, and various types of cancer.