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.

Question

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.

Quizplus · Accepted Answer

The Answer is i)

\mathrm { H } _ { 0 } : \mathrm { p } _ { 0 } = \mathrm { p } _ { 1 } = \ldots = \mathrm { p } _ { 7 } = 1 / 7 . \mathrm { H } _ { 1 } :

At least one of these probabilities is different from the others. The value of the test statistic is

\chi ^ { 2 } = 2.4

, which is less than the critical value of

\chi ^ { 2 } = 12.59

. We fail to reject the null hypothesis.
ii) The value of the test statistic is

\chi ^ { 2 } = 579.5

, which is greater than the critical value of

\chi ^ { 2 } = 12.59

. We reject the null hypothesis. An outlier has a significant effect on the

\chi ^ { 2 }

test statistic. Use a 2 test to test the claim that in the given contingency table, the row variable and the column variable are
independent.

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

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