A researcher believes that arrivals at a walk-in hair salon are Poisson distributed.The following data represent a distribution of frequency of arrivals in a one-hour time period. $$\begin{array} { | l | l | l | l | l | l | l | }
\hline \text { Number of customer arrivals } & 0 & 1 & 2 & 3 & 4 & \geq 5 \
\hline \text { Frequency } & 47 & 56 & 39 & 22 & 18 & 10 \
\hline
\end{array}$$ Using $\alpha$= 0.10, the critical chi-square value for this goodness-of-fit test is _______.

Question

A researcher believes that arrivals at a walk-in hair salon are Poisson distributed.The following data represent a distribution of frequency of arrivals in a one-hour time period. $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Number of customer arrivals } & 0 & 1 & 2 & 3 & 4 & \geq 5 \
\hline \text { Frequency } & 47 & 56 & 39 & 22 & 18 & 10 \
\hline
\end{array}$$ Using $\alpha$= 0.10, the critical chi-square value for this goodness-of-fit test is _______.

Quizplus · Accepted Answer

The critical chi-square value for a goodness-of-fit test depends on the significance level (in this case, 0.10) and the degrees of freedom. The degrees of freedom for a chi-square test in this context are calculated as the number of categories minus 1 minus the number of parameters estimated from the data. Since there are 6 categories (0, 1, 2, 3, 4, ≥5) and we estimate one parameter (the mean arrival rate), the degrees of freedom are 6 - 1 - 1 = 4. Looking up the critical value for 4 degrees of freedom at a 0.10 significance level in a chi-square distribution table gives us 7.779.

A Researcher Believes That Arrivals at a Walk-In Hair Salon