Two of the variables in this data set are the weight of the vehicle and the city miles per gallon. We wish to test whether there is statistically significant evidence of a negative correlation between weight and city mpg. A randomization distribution based on the data is shown below.
(a) (3 points) Write the null and alternative hypotheses.
(b) (3 points) What is the correct notation for the sample statistic?
(c) (4 points) Which of the following sample statistics would give statistically signifi cant evidence at the α = 0.05 level for the alternative hypothesis? (-0.75, -0.4, -0.1, 0, 0.1, 0.4, 0.75)
2. (15 points) Some researchers were interested in whether the antidepressant drug de sipramine reduces the likelihood of relapse among cocaine addicts who are actively trying to quit. 48 subjects were randomly assigned to either a fixed daily dose of desipramine or a fixed daily dose of a placebo. After six months, it was determined whether or not the subject relapsed. At the conclusion of the study, the researchers looked to see if the proportion of the desipramine group who relapsed was significantly lower that the proportion of the placebo group. In parts (a) through (c) below, give a formal decision (reject H0 or fail to reject H0) for the test using a significance level of α = 0.05.
(a) (2 points) The p-value was 0.023.
(b) (2 points) The p-value was 0.503.
(c) (2 points) The p-value was 0.001.
(d) (3 points) Which of the p-values in parts (a) through (c) provides the strongest evidence for the alternative hypothesis?
(e) (3 points) Which of the p-values in parts (a) through (c) provides the weakest evidence for the alternative hypothesis?
(f) (3 points) How do your formal decisions change in parts (a) through (c) change if the researchers make their conclusions using a significance level of α = 0.01?
3. (12 points) Indicate whether each question is best assessed by using a confidence interval or a hypothesis test. For a hypothesis test, write hypotheses and use correct parameter notation. For a confidence interval, write the correct notation for the parameter that we are trying to estimate. You do not need to define the parameter.
(a) (3 points) Is there a difference between the mean number of hours spent watching TV per week by full-time female college students and the mean number of hours spent watching TV per week by full-time male students?
(b) (3 points) What is the mean time for getting through the intersection of Pleasant Valley Road and Riverside Drive in East Austin?
(c) (3 points) Is the proportion of women who have at least one tattoo different from the proportion of men who have at least one tattoo?
(d) (3 points) What percent of US adults support the death penalty?
4. (6 points) We have data from a random sample of elementary statistics students at a large college. We are interested in whether the mean SAT math score for all elementary statistics students at this college is different than the national average of 527 (the 527 is a parameter).
(a) (3 points) State the appropriate null and alternative hypotheses.
(b) (3 points) I computed a 95% confidence interval for the mean SAT math score from the data: [602.188, 616.532]. What is the conclusion in context of the hypothesis test at the α = 0.05 level? Explain how you arrived at your answer. (I do not want a novel. A sentence or two will suffice.)
5. (6 points) Say researchers are interested in scores on the math portion of the SAT for a particular school. For each graph of side-by-side dotplots, indicate which of the two samples shows stronger evidence that the mean is less than 500. If they show about the same strength of evidence, indicate that.6. (6 points) The Gallup organization surveyed 1100 adult Americans in 2002 and con ducted an independent survey of 1100 adult Americans in 2014. In both surveys they asked the following question: “Right now, do you think the state of moral values in the country as a whole is getting better or worse?”Researchers were interested in whether the proportion of all adult Americans who would respond “yes”changed between 2002 and 2014.
(a) (3 points) Write the appropriate null and alternative hypotheses.
(b) (3 points) The researchers report: “the test of a difference in proportions results in a p-value of 0.00022.”Do you think this provides sufficient evidence that the proportion of Americans who would respond “yes”to the question changed between 2002 and 2014 or do you think our observed difference occurred just by chance? Provide a short explanation.
