Q1 [2 pts]: The graph below shows the sampling distributions of two estimators for the parameter (). The dashed line represents the distribution of Estimator 1 and the solid line represents the distribution of Estimator 2. Which of the following statements is correct?

Q2 [2 pts]: Suppose we use the same data to construct the 95% and the 99% confidence intervals for the population proportion. Which of the following statements is correct?

Q19 [2 pts]: Under the null hypothesis, what distribution does the test statistic have? Please name the distribution and provide its parameter value(s).

Q12 [3 pts]: Calculate the test statistic value. Please show your work. You can write your final answer in the calculator-ready form.

2f. Use your results to describe the relationship between the types of praise and multiplication scores. In your answer indicate whether the multiplication scores differed for the two groups, and if the scores differed describe the specific difference that was found.

2a. If the teacher wants to test the prediction that the two groups will differ, how should the null and alternative hypotheses be stated?

2d. What is the correct conclusion to draw about the null hypothesis?

Q11 [2 pts]: When checking whether the sample size is large enough for running the hypothesis test, the committee made the following statement: “In the sample, 14 packages contained the Billy Wonka cards and 86 did not. Since 14 is less than 15, the sample size condition for the hypothesis test is not met.” Identify the error in the way that the committee checked the sample size and show that the sample size is in fact large enough for running the hypothesis test.

3a. If a researcher wants to test the prediction that taking Prozac improves the participants well-being scores, what are the correct null and alternative hypotheses?

Problem 2 – Independent Groups t-test An elementary school teacher is trying to figure out the best way to motivate her students to learn multiplication. The teacher understands that rewarding students with praise is an effective strategy for motivating students, but she is unsure whether praise should come after each correct response or after correctly answering a series of questions (delayed reward). To test which strategy is most effective the teacher randomly divides her class into two groups. Half of the students receive praise each time they correctly answer a question, and the other half receive no praise until the end of the assignment. After using these two strategies for a few days the teacher then gives all of her students a multiplication test. Use this information to answer questions 2a-2i below.