What is the probability that in 5 rolls of the Pass the Pigs pig die, you will get a Trotter (pig lands on its feet) two times?  SHOW WORK. 

Situation A:  You take out one ball from the bag.  After you put the first ball back into the bag, you take a second ball from the bag. What is the probability that Event 1 AND Event 2 happen?  Show your work. Event 1: The first ball is red. Event 2: The second ball is green.

I pledge that I am not cheating in any way on this test.  I am not having another person complete the exam for me.  I am not interacting with any other person.  I am not accessing resources online.  I may use my notes but understand that I have limited time to complete the sections of the test, and looking through notes may prevent me from completing the test in the time allowed.  Reminder that the points on this test are meaningless; you are being assessed based on the standards.

Many graduate school programs in the United States require people who apply to take the Graduate Record Exam (GRE). One part of the GRE, the GRE-Quantitative test, assesses students’ levels of quantitative reasoning and thinking. The highest score possible on the GRE-Quantitative test is a score of 800. When a student scores 700 or higher on the GRE-Quantitative test, graduate schools programs believe that the student has strong quantitative skills. The table below shows the students who took the GRE Quantitative test between 2003 and 2006. The table is organized according to one of four graduate school majors: Economics, Political Science, Psychology or Sociology. A statistics student conducted a chi-square test for independence. The result was a p-value less than 0.0001.  Which of the following is the most appropriate conclusion that the student should make?

A police officer claims that 50% of all car accidents occur Mondays through Thursdays, 15% on Fridays, 20% on Saturdays and 15% on Sundays. To test his claim, the officer decides to take a random sample of 50 accidents that happened over the past year. He records the days that the 50 accidents occurred. The results are presented in the table below. Are the conditions met in order to conduct a chi-square goodness-of-fit test?

Which one of the following best explains the confidence interval that is listed in the output?

The 0.9% difference in improvement rates is not statistically significant (p-value = 0.88).  What does the phrase “not statistically significant” tell us in this study’s context?

What is the relationship between lung cancer and smoking?  Many researchers are studying this issue.  A researcher placed 1,000 randomly selected adults who smoke into 2 groups: light smokers and heavy smokers. He followed their progress for 10 years.  At the end of the ten-year period, he identified the proportion of people, in each group, who had developed lung cancer. His null hypothesis was that people in both groups would have the same incidence rate…that is, would be equally likely to develop lung cancer. The p-value is found to be smaller than the level of significance. What is the most appropriate conclusion?

Using the margin of error given in the previous problem, which of the following is the 99% confidence interval for the true difference between the 2016 and 2021 groups?  Recall that the sample proportion from 2016 was 57% and the sample proportion in 2021 was 60%.  Let p16 represent the true proportion in 2016 and p21 represent the true proportion in 2021. You should be finding the confidence interval for p16 – p21 .

A Canadian study measuring depression level in teens (as reported in the Journal of Adolescence, vol. 25, 2002) randomly sampled 112 male teens and 101 female teens, and scored them on a common depression scale (higher score representing more depression). The researchers suspected that the mean depression score for male teens is higher than for female teens, and wanted to check whether data would support this hypothesis. If μ1 and μ2 represent the mean depression score for male teens and female teens respectively, which of the following is the appropriate pair of hypotheses in this case?