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A national health survey weighed a sample of 546546 boys aged 6116-11 and found that 7474 of them were overweight. They weighed a sample of 455455 girls aged 6116-11 and found that 7575 of them were overweight. Can you conclude that the proportion of boys who are overweight is less than the proportion of girls who are overweight? \newlineLet p1p_{1} denote the proportion of boys who are overweight and let p2p_{2} denote the proportion of girls who are overweight. \newlineUse the α=0.10\alpha=0.10 level of significance and the p-value p_{\text{-value }}.

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Q. A national health survey weighed a sample of 546546 boys aged 6116-11 and found that 7474 of them were overweight. They weighed a sample of 455455 girls aged 6116-11 and found that 7575 of them were overweight. Can you conclude that the proportion of boys who are overweight is less than the proportion of girls who are overweight? \newlineLet p1p_{1} denote the proportion of boys who are overweight and let p2p_{2} denote the proportion of girls who are overweight. \newlineUse the α=0.10\alpha=0.10 level of significance and the p-value p_{\text{-value }}.
  1. State hypotheses: State the null and alternate hypotheses for comparing two proportions.\newlineTo test if the proportion of overweight boys is less than the proportion of overweight girls, we set up the hypotheses as follows:\newlineNull Hypothesis H0H_0: The proportion of overweight boys is equal to or greater than the proportion of overweight girls. Mathematically, this is expressed as p1p2p_1 \geq p_2.\newlineAlternate Hypothesis H1H_1: The proportion of overweight boys is less than the proportion of overweight girls, expressed as p_1 < p_2.

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