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 $p = 1 / 2$ =

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Definitions:

Transition Metal Elements

Elements found in groups 3 through 12 of the periodic table, characterized by their ability to form stable compounds with variable oxidation states.

Ionic

Relating to or involving ions, typically describing chemical bonds formed through the electrostatic attraction between oppositely charged ions.

Coordinate Covalent

A type of chemical bond where both electrons come from the same atom, typically seen in complex ions or molecules where a metal atom is bonded to one or more ligands.

Alkaline Earth Elements

A group of elements in the periodic table comprising beryllium, magnesium, calcium, strontium, barium, and radium, characterized by their two valence electrons.