Recent studies have found that Australian children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television.
\begin{tabular}{|c|c|c|c|c|}
\hline & & \multicolumn{3}{|c|}{ TV Hours } \
\hline & & $0-3$ hours & $3-6$ hours & $6+$ hours \
\hline \multirow{4}{*}{ Weights } & More than 10kg overweight & 1 & 9 & 20 \
\cline { 2 - 6 } & Within 10kg of normal weight & 20 & 15 & 15 \
\cline { 2 - 6 } & More than 10kg underweight & 10 & 5 & 5 \
\hline
\end{tabular}

You are interested in testing whether the average number of hours spent watching TV and weights are independent at the $1 \%$ level of significance. If the weights and mean number of hours spent watching TV are independent, what is the expected number of children who spend more than 6 hours on average watching TV and are more than $10 \mathrm{~kg}$ overweight?

Answer: $\square$ (Please provide your answer to 1 decimal place).

Question

Recent studies have found that Australian children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television.
\begin{tabular}{|c|c|c|c|c|}
\hline & & \multicolumn{3}{|c|}{ TV Hours } \
\hline & & $0-3$ hours & $3-6$ hours & $6+$ hours \
\hline \multirow{4}{*}{ Weights } & More than 10kg overweight & 1 & 9 & 20 \
\cline { 2 - 6 } & Within 10kg of normal weight & 20 & 15 & 15 \
\cline { 2 - 6 } & More than 10kg underweight & 10 & 5 & 5 \
\hline
\end{tabular}

You are interested in testing whether the average number of hours spent watching TV and weights are independent at the $1 \%$ level of significance. If the weights and mean number of hours spent watching TV are independent, what is the expected number of children who spend more than 6 hours on average watching TV and are more than $10 \mathrm{~kg}$ overweight?

Answer: $\square$ (Please provide your answer to 1 decimal place).

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the total number of children surveyed. ‖ ‖ step 2 ⋮ Determine the marginal totals for each row and column. ‖ ‖ step 3 ⋮ Calculate the expected frequency for children more than 10kg overweight and watching more than 6 hours of TV. ‖ ‖ step 4 ⋮ Use the formula for expected frequency: $E_{ij} = \frac{(row~total) imes (column~total)}{grand~total}$. ‖ ‖ step 5 ⋮ Plug in the values to find the expected frequency for the specified cell. ‖ ∻Answer∻ ⚹ [Insert final answer here] ⚹ ∻Key Concept∻ ⚹Chi-Square Test of Independence⚹ ∻Explanation∻ ⚹The expected frequency is calculated to determine if there is a significant association between two categorical variables in a contingency table.⚹◊What is the formula for calculating the expected number of children for a contingency table in statistics?⍭ Generate me a similar question◊

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