In a research study examining the impact of fast-food consumption on dietary and health characteristics, researchers provided summary statistics on the daily calorie intake for a representative sample of teens who do not typically eat fast food and a representative sample of teens who do eat fast food. The data is summarized in the table below:| Sample | Sample Size | Sample Mean | Sample Standard Deviation ||------------------------|-------------|-------------|---------------------------|| Do not eat fast food | 666 | 2,256 | 1,514 || Eat fast food | 414 | 2,631 | 1,138 |The research question is whether the mean calorie intake for teens who typically eat fast food is greater than the mean intake for those who do not by more than 150 calories per day. We are testing this hypothesis with a significance level of \( \alpha = 0.05 \). We denote \( \mu_1 \) as the mean calorie intake for teens who typically eat fast food, and \( \mu_2 \) as the mean calorie intake for teens who do not typically eat fast food.1. **State the appropriate null and alternative hypotheses:** - \( H_0: \mu_1 - \mu_2 = 0 \) - \( H_a: \mu_1 - \mu_2 > 150 \) Other choices for hypotheses are as follows (though they are not correct for this specific research question): - \( H_0: \mu_1 - \mu_2 > 150 \) - \( H_a: \mu_1 - \mu_2 > 150 \) - \( H_0: \mu_1 - \mu_2 > 0 \) - \( H_a: \mu_1 - \mu_2 > 150 \) - \( H_0: \mu_1 - \mu_2 = 150 \) - \( H_a: \mu_1 - \mu_2 > 150 \) - \( H_0: \mu_1 - \mu_2 = 0 \) - \( H_a: \mu_1 - \mu_2 = 150 \)2. **Find the test statistic and P-value.** Use a table or technology to find these values. Round your

Name: In a research study examining the impact of fast-food consumption on
Uploaded: 2024-03-20T07:07:50.000Z
Channel: Bartleby
Description: In a research study examining the impact of fast-food consumption on dietary and health characteristics, researchers provided summary statistics on the daily calorie intake for a representative sample of teens who do not typically eat fast food and

It is given that the summary statistics of sample of teens who do not typically eat fast food and…

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What impact does fast-food consumption have on various dietary and health characteristics? A research article reported the accompanying summary statistics on daily calorie intake for a representative sample of teens who do not typically eat fast food and a representative sample of teens who do eat fast food. Sample Size Sample Mean Sample Standard Deviation Sample Do not eat fast food 666 2,256 1,514 Eat fast food 414 2,631 1,138 Is there convincing evidence that the mean calorie intake for teens who typically eat fast food is greater than the mean intake for those who don't by more than 150 calories per day? (Test the relevant hypotheses using a significance level of a = 0.05. Use u, for teens who typically eat fast food and u, for teens who don't typically eat fast food.) State the appropriate null and alternative hypotheses. O Ho: H1 - H2 = 0 Hạ: H1 - 42 > 150 O Ho: H1 - H2 > 150 Hgi Hy - H2 = 0 Ho: H1 - H2 = 150 H2i H1 - H2> > 150 Ho: H1 - H2 = Hại H1 - H2>0 O Ho: H1 - H2 > 150 Hai H1- H2 = 150 Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. We fail to reject Ho. There is not convincing evidence that the mean calorie intake for teens who typically eat fast food is greater than the mean intake for those who don't by more than 150 calories per day. We reject H.: There is not convincing evidence that the mean calorie intake for teens who typically eat fast food is greater than the mean intake for those who don't by more than 150 calories per day. O We fail to reject Ho. There is convincing evidence that the mean calorie intake for teens who typically eat fast food is greater than the mean intake for those who don't by more than 150 calories per day. We reject Ho. There is convincing evidence that the mean calorie intake for teens who typically eat fast food is greater than the mean intake for those who don't by more than 150 calories per day.