Question

Math

Posted 6 months ago

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A media streaming website knows that $70 \%$ of its customers primarily watch on their television, $18 \%$ primarily watch on their computer, and $12 \%$ primarily watch on a mobile device. The company wonders if these percentages hold true after a recent update to the product. They take a random sample of 700 customers and obtain these results:
\begin{tabular}{lrrr}
Device & Television & Computer & Mobile \\
\hline Expected & $70 \%$ & $18 \%$ & $12 \%$ \\
\# of customers & 401 & 197 & 102
\end{tabular}
They want to perform a $\chi^{2}$ goodness-of-fit test to determine if these results suggest that the the distribution has changed.
What is the expected count of customers that watch on their computer in the sample?
You may round your answer to the nearest hundredth.
Expected:
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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

Calculate the expected count of customers watching on their computer using the given percentage and sample size

step 2

The expected percentage for the computer is $18\%$

step 3

The sample size is 700 customers

step 4

Multiply the sample size by the expected percentage for the computer: $700 \times 0.18$

step 5

Perform the calculation: $700 \times 0.18 = 126$

step 6

Round the answer to the nearest hundredth, which in this case does not change the value: $126.00$

Answer

The expected count of customers that watch on their computer in the sample is 126.00.

Key Concept

Expected Count in a Chi-Square Test

Explanation

The expected count is calculated by multiplying the total sample size by the expected percentage for each category. This is a step in performing a Chi-Square goodness-of-fit test.

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