Statistics Final Name: 1. The paper ”Cigarette Tar Yields in Relation to Mortality from Lung Cancer in the Cancer Prevention Study II Prospective Cohort” (British Medical Journal [2004]: 72–79)...

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Statistics Final Name: 1. The paper ”Cigarette Tar Yields in Relation to Mortality from Lung Cancer in the Cancer Prevention Study II Prospective Cohort” (British Medical Journal [2004]: 72–79) included the accompanying data on the tar level of cigarettes smoked for a sample of male smokers who died of lung cancer. Tar Level Frequency Low 103 Medium 378 High 563 Very High 150 Assume the sample is representative of male smokers who die of lung cancer. Test the claim that the proportion of male smoker lung cancer deaths is not the same for the four tar level categories? (a) (2 points) Write the null and alternative hypotheses. (b) (1 point) What formula should be used for the test statistic? (b) (c) (1 point) What number is the test statistic equal to? Round to the thousandths. (c) (d) (1 point) Draw a picture of the Chi-Square Distribution (centered at df=number of categories minus 1), and mark the location of your test statistic value along the x-axis in the right tail of your graph. (e) (1 point) What p-value do you obtain? Round to the ten-thousandths. (e) (f) (1 point) Do you reject the null hypothesis or fail to reject the null hypothesis? Explain. (g) (1 point) State a full sentence conclusion stating the decision you made. 2. Are babies born to mothers who use assistive reproduction technology (ART) more likely to be born prematurely than babies conceived naturally? The data in the accompanying table are from the paper ”Child Growth from Birth to 18 months After Assisted Reproduction Technology” (International Journal of Nursing [2010]: 1159–1166). The data are from a random sample of 19,614 births. Each birth was classified according to whether the mother used ART and whether the baby was premature. Use these data to decide if there is convincing evidence of an association between the use of ART and whether or not a baby is premature. Use α = 0.01. conceived conceived using ART naturally Premature 154 2405 Not Premature 212 18,843 (a) (2 points) Write the null and alternative hypotheses. (b) (1 point) What formula should be used for the test statistic? (c) (1 point) What number is the test statistic equal to? Round to the thousandths (d) (1 point) Draw a picture of the Chi-Square Distribution, centered at df = (R − 1)(C − 1), and mark the location of your test statistic value along the x-axis in the right tail of your graph. (e) (1 point) What p-value do you obtain? Round to the ten-thousandths. (f) (1 point) Do you reject the null hypothesis or fail to reject the null hypothesis? Explain. (g) (1 point) State a full sentence conclusion stating the decision you made. 3. Do people feel hungrier after sampling a healthy food? The authors of the paper ”When Healthy Food Makes You Hungry” (Journal of Consumer Research [2010]: S34–S44) carried out a study to answer this question. They randomly assigned vol- unteers into one of three groups. The people in the first group were asked to taste a snack that was billed as a new health bar containing high levels of protein, vitamins, and fiber. The people in the second group were asked to taste the same snack but were told it was a tasty chocolate bar with a raspberry center. After tasting the snack, participants were asked to rate their hunger level on a scale from (not at all hungry) to (very hungry). The people in the third group were asked to rate their hunger but were not given a snack. The data in the accompanying table are consistent with summary quantities given in the paper (although the sample sizes in the actual study were larger). Do these data provide evidence that the mean hunger rating differs for at least two of the treatments (”healthy” snack, ”tasty” snack, no snack)? Test the relevant hypotheses using a significance level of α = 0.05. (a) (1 point) What statements represent the null and alternative hypotheses? (b) (1 point) What is the formula for the test statistic? (b) (c) (1 point) What is the value of the test statistic? Round to the thousandths. (c) (d) (1 point) What p-value is obtained from performing one-way ANOVA test? Round to the ten-thousandths. (d) (e) (1 point) Sketch a graph of the sampling distribution AND the p-value HERE. (f) (1 point) Did you reject H0 or fail to reject H0? (f) (g) (1 point) Interpret the decision. State a full sentence conclusion explaining the decision you made.