The following table shows the number of employees who called in sick at a business for
different days of a particular week. $$\begin{array} { r | c c c c c c c }
\text { Day } & \text { Sun } & \text { Mon } & \text { Tues } & \text { Wed } & \text { Thurs } & \text { Fri } & \text { Sat } \
\hline \text { Number sick } & 8 & 12 & 7 & 11 & 9 & 11 & 12
\end{array}$$ 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

The following table shows the number of employees who called in sick at a business for
different days of a particular week. $$\begin{array} { r | c c c c c c c } 
\text { Day } & \text { Sun } & \text { Mon } & \text { Tues } & \text { Wed } & \text { Thurs } & \text { Fri } & \text { Sat } \
\hline \text { Number sick } & 8 & 12 & 7 & 11 & 9 & 11 & 12
\end{array}$$ 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)

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

The Following Table Shows the Number of Employees Who Called