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

question 23

Essay

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent
-The following table shows the number of employees who called in sick at a business for different days of a particular week. $$\begin{array} { l | l l l l l l l } \text { Day } & \text { Sun}& \text { Mon }& \text {tues}& \text { Wed }&\text { Thurs }& \text { Fri }& \text { Sat } \\\hline \text { Number sick } & 8 & 12 & 7 & 11 & 9 & 11 & 12\end{array}$$ i)At the 0.05 level of significance, test the claim that sick days occur with equal frequency on the different days of the week. ii)Test the claim after changing the frequency for Saturday to 152. Describe the effect of this outlier on the test.

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Definitions:

Geometric Mean

The central tendency of a set of numbers that is calculated by taking the nth root (where n is the count of numbers) of the product of the values.

Weighted Mean

The mean obtained by assigning each observation a weight that reflects its importance.

Arithmetic Mean

The sum of a set of numerical values divided by the number of values, commonly referred to as the average.

Standard Deviations

A measure of the dispersion or spread of a set of numbers, showing how much variation exists from the average.