Jacqueline works as a quality control expert at a factory that packages different chocolates in variety packs. She selected a random container to see how well the 220 chocolates inside matched the advertised distribution. The table below shows the advertised distribution and the observed counts for each type of chocolate in the container she selected.
\begin{tabular}{lrrrr}
Type of chocolate & Dark & Milk & Salted caramel & White \
\hline Advertised & $40 \%$ & $30 \%$ & $20 \%$ & $10 \%$ \
\# of chocolates observed & 81 & 75 & 48 & 16
\end{tabular}

Jacqueline wants to perform a $\chi^{2}$ goodness-of-fit test to determine if these results suggest that the actual distribution of chocolates doesn't match the advertised distribution.

What is the expected count of salted caramel chocolates in Jacqueline's sample?
You may round your answer to the nearest hundredth.
Expected: $\square$

Question

Jacqueline works as a quality control expert at a factory that packages different chocolates in variety packs. She selected a random container to see how well the 220 chocolates inside matched the advertised distribution. The table below shows the advertised distribution and the observed counts for each type of chocolate in the container she selected.
\begin{tabular}{lrrrr} 
Type of chocolate & Dark & Milk & Salted caramel & White \
\hline Advertised & $40 \%$ & $30 \%$ & $20 \%$ & $10 \%$ \
\# of chocolates observed & 81 & 75 & 48 & 16
\end{tabular}

Jacqueline wants to perform a $\chi^{2}$ goodness-of-fit test to determine if these results suggest that the actual distribution of chocolates doesn't match the advertised distribution.

What is the expected count of salted caramel chocolates in Jacqueline's sample?
You may round your answer to the nearest hundredth.
Expected: $\square$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the expected count of salted caramel chocolates, we first need to determine the total number of chocolates in the sample, which is given as 220. ‖ ‖ step 2 ⋮ The advertised percentage for salted caramel chocolates is 20%. To find the expected count, we multiply the total number of chocolates by the advertised percentage: $$ \text{Expected count} = 220 \times 0.20 $$ ‖ ‖ step 3 ⋮ Performing the multiplication: $$ \text{Expected count} = 220 \times 0.20 = 44 $$ ‖ ∻Answer∻ ⚹ The expected count of salted caramel chocolates is 44. ⚹ ∻Key Concept∻ ⚹Expected count calculation⚹ ∻Explanation∻ ⚹The expected count is found by multiplying the total number of chocolates by the advertised percentage for the specific type of chocolate.⚹◊What is the formula for calculating the expected count in a $\chi^{2}$ goodness-of-fit test?⍭ Generate me a similar question◊

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