Consider a study testing whether birds were equally likely to rest on each streetlight. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) What is the ?² value we would obtain for a goodness-of-fit test comparing these data to the expectations from a Poisson process?
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$\begin{array}{|cc|}\hline \begin{array}{l}\text { Number } \\\underline {\text { birds }}\end{array} & \begin{array}{l}\text { Number } \\\underline {\text { of lights }}\end{array} \\0 & 3 \\1 & 12 \\2 & 9 \\\geq 3 & 6 \\\hline\end{array}$

Question

Consider a study testing whether birds were equally likely to rest on each streetlight. Researchers surveyed 30 randomly chosen streetlights in a city known to have many birds and counted the number of birds resting on each streetlight. Data on the number of birds seen on the lights are shown. (Note: No lights had more than three birds.) What is the ?² value we would obtain for a goodness-of-fit test comparing these data to the expectations from a Poisson process?
?

\begin{array}{|cc|}\hline \begin{array}{l}\text { Number } \\\underline {\text { birds }}\end{array} & \begin{array}{l}\text { Number } \\\underline {\text { of lights }}\end{array} \\0 & 3 \\1 & 12 \\2 & 9 \\\geq 3 & 6 \\\hline\end{array}

Quizplus · Accepted Answer

The chi-square value is calculated by comparing observed frequencies with expected frequencies under a Poisson distribution. The expected frequencies are calculated based on the average rate (λ) of birds per light. The chi-square statistic is the sum of the squared differences between observed and expected frequencies, divided by the expected frequencies. The calculations lead to a chi-square value of 6.33.

Consider a Study Testing Whether Birds Were Equally Likely to Rest