A company wants to determine if its employees have any preference among 5 different health plans which it offers to them. A sample of 200 employees provided the data below. Calculate the chi-square test statistic $x ^ { 2 }$ to test the claim that the probabilities show no preference. Use $\alpha$

=0.01 .
$\begin{array} { l | c l l l l }
\text { Plan } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Employees } & 65 & 32 & 18 & 55 & 30
\end{array}$
A) 37.45
B) 45.91
C) 48.91
D) 55.63

Question

A company wants to determine if its employees have any preference among 5 different health plans which it offers to them. A sample of 200 employees provided the data below. Calculate the chi-square test statistic

x ^ { 2 }

to test the claim that the probabilities show no preference. Use

\alpha

=0.01 .

\begin{array} { l | c l l l l } \text { Plan } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Employees } & 65 & 32 & 18 & 55 & 30\end{array}

=0.01 .
$\begin{array} { l | c l l l l } 
\text { Plan } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Employees } & 65 & 32 & 18 & 55 & 30
\end{array}$
A)  37.45 
B)  45.91 
C)  48.91 
D)  55.63

Quizplus · Accepted Answer

The chi-square test statistic $x^2$ is calculated using the formula $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ is the observed frequency and $E_i$ is the expected frequency. If there's no preference among the 5 plans, each plan is expected to be chosen by an equal number of employees, so $E_i = \frac{200}{5} = 40$ for each plan. Calculating $\chi^2$ gives:$$\chi^2 = \frac{(65-40)^2}{40} + \frac{(32-40)^2}{40} + \frac{(18-40)^2}{40} + \frac{(55-40)^2}{40} + \frac{(30-40)^2}{40} = 37.45$$

A Company Wants to Determine If Its Employees Have Any x2x ^ { 2 }x2

A Company Wants to Determine If Its Employees Have Any $x ^ { 2 }$