A zoo has separate habitats for its three types of bears: brown, black, and grizzly bears. Each habitat offers three areas for the bears to spend their time: an outdoor area, an indoor area, and a pool.

Gisele is the zookeeper who cares for the brown bear. She takes a random sample of 10 moments each day for a week and records which area the brown bear is at each of those moments. Bryan and Adele use a similar strategy and obtain separate samples of 70 observations for the black and grizzly bears, respectively. Here are their results:
\begin{tabular}{lrrrr}
Bear & Outdoor & Indoor & Pool & Total \
\hline Brown & 23 & 27 & 20 & 70 \
Black & 15 & 18 & 37 & 70 \
Grizzly & 32 & 12 & 26 & 70 \
Total & 70 & 57 & 83 & 210
\end{tabular}

They want to perform a $\chi^{2}$ test for homogeneity to judge if the bears are spending their time differently in their habitats.

What is the expected count for the cell corresponding to the grizzly bear being by the pool?
You may round your answer to the nearest hundredth.
Expected:

Question

A zoo has separate habitats for its three types of bears: brown, black, and grizzly bears. Each habitat offers three areas for the bears to spend their time: an outdoor area, an indoor area, and a pool.

Gisele is the zookeeper who cares for the brown bear. She takes a random sample of 10 moments each day for a week and records which area the brown bear is at each of those moments. Bryan and Adele use a similar strategy and obtain separate samples of 70 observations for the black and grizzly bears, respectively. Here are their results:
\begin{tabular}{lrrrr} 
Bear & Outdoor & Indoor & Pool & Total \
\hline Brown & 23 & 27 & 20 & 70 \
Black & 15 & 18 & 37 & 70 \
Grizzly & 32 & 12 & 26 & 70 \
Total & 70 & 57 & 83 & 210
\end{tabular}

They want to perform a $\chi^{2}$ test for homogeneity to judge if the bears are spending their time differently in their habitats.

What is the expected count for the cell corresponding to the grizzly bear being by the pool?
You may round your answer to the nearest hundredth.
Expected:

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the expected count for the grizzly bears by the pool, we use the formula for expected counts in a chi-square test for homogeneity: $E_{ij} = \frac{(Row\ Total) imes (Column\ Total)}{Grand\ Total}$. ‖ ‖ step 2 ⋮ The row total for grizzly bears is 70, the column total for the pool is 83, and the grand total is 210. ‖ ‖ step 3 ⋮ Plugging these values into the formula gives us: $E_{ ext{grizzly, pool}} = \frac{(70) imes (83)}{210}$. ‖ ‖ step 4 ⋮ Using the asksia-ll calculation list, we simplify the expression: $(70 imes 83) / 210 = 27 \frac{2}{3}$. ‖ ‖ step 5 ⋮ Rounding to the nearest hundredth, we get: $27.67$. ‖ ∻Answer∻ ⚹ 27.67 ⚹ ∻Key Concept∻ ⚹Expected Count in a Chi-Square Test for Homogeneity⚹ ∻Explanation∻ ⚹The expected count is calculated by multiplying the row and column totals and then dividing by the grand total. This value is used to compare observed counts with expected counts in a chi-square test.⚹◊What is the formula to calculate the expected count for a cell in a $\chi^{2}$ test for homogeneity?⍭ Generate me a similar question◊

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