(Solved): An article reported that heart attack risk could be reduced by taking aspirin. This conclusion was ...

An article reported that heart attack risk could be reduced by taking aspirin. This conclusion was based on a designed experiment involving both a control group of individua that took a placebo having the appearance of aspirin but known to be inert and a treatment group that took aspirin according to a specified regimen. Subjects were random assigned to the groups to protect against any biases and so that probability-based methods could be used to analyze the data. Of the 11,034 individuals in the control grour 199 subsequently experienced heart attacks, whereas only 104 of the 11,037 in the aspirin group had a heart attack. Calculate an interval of plausible values for \( \theta \) at the 95\% confidence level. (Use \( p_{1} \) for the control group and \( p_{2} \) for the aspirin treatment group. Round your answers to four decimal places.) What does this interval suggest about the efficacy of the aspirin treatment? We are \( 95 \% \) confident that people who take the aspirin treatment are proportionally more likely, by an amount within the interval, to suffer a heart attack than those who do not. This suggests aspirin therapy may be effective in reducing the risk of a heart attack. We are \( 95 \% \) confident that people who do not take the aspirin treatment are proportionally more likely, by an amount within the interval, to suffer a heart attack than those who do. This suggests aspirin therapy may actually increase the risk of a heart attack. We are \( 95 \% \) confident that people who take the aspirin treatment are proportionally more likely, by an amount within the interval, to suffer a heart attack than those who do not. This suggests aspirin therapy may actually increase the risk of a heart attack. We are \( 95 \% \) confident that people who do not take the aspirin treatment are proportionally more likely, by an amount within the interval, to suffer a heart attack than those who do. This suggests aspirin therapy may be effective in reducing the risk of a heart attack. Toxaphene is an insecticide that has been identified as a pollutant in the Great Lakes ecosystem. To investigate the effect of toxaphene exposure on animals, groups of rats were given toxaphene in their diet. A study reports weight gains (in grams) for rats given a low dose (4 ppm) and for control rats whose diet did not include the insecticide. The sample standard deviation for 21 female control rats was \( 29 \mathrm{~g} \) and for 16 female low-dose rats was \( 52 \mathrm{~g} \). Does this data suggest that there is more variability in low-dose weight gains than in control weight gains? Assuming normality, carry out a test of hypotheses at significance level \( 0.05 \). State the relevant hypotheses. (Use \( \sigma_{1} \) for low-dose treatment and \( \sigma_{2} \) for control condition.) \[ \begin{array}{c} H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{a}: \sigma_{1}^{2}>\sigma_{2}^{2} \\ H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{a}: \sigma_{1}^{2} \geq \sigma_{2}^{2} \\ H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{a}: \sigma_{1}^{2}<\sigma_{2}^{2} \\ H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{a}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \end{array} \] Calculate the test statistic. (Round your answer to two decimal places.) \[ f=1.96 \]