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Q21 [3 pts]: Solve the sample standard deviation (i.e., the standard deviation of the number of disposable containers used by a student each day based on the sample). Please show your work. You can write your final answer in the calculator-ready form. Hint: use the test statistic and the sample mean in the output.

Q17 [2 pts]: An expert claimed that p was in the neighborhood of 70%. If we use 70% as the estimate of p in the sample size calculation, will a larger or smaller sample be required? There is no need to explain.

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?

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.

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?

A patient presents to the clinic with complaints of increased anxiety and states, “I feel like someone is following me.” The patient is restless. The initial vitals are: HR 126, BP 156/90. The patient has poor dentition and has several “poc” marks and open wounds to arms and cheeks. The nurse suspects chronic use of what substance? 

I understand that this exam is to be completed individually and that I will have 120 minutes to complete the exam. I understand that I am not allowed to discuss or share the questions in this test or my answers to this test with anyone, nor am I allowed to receive help, input, or guidance from others (including all forms of AI) while taking this test and that all answers are to be 100% my own work. I understand that if it is found that I collaborated with others or cheated on any portion of this test a grade of 0 will be assigned and a student code of conduct referral will be submitted.    Name [name] date [date]

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.

2b. Use the data in the table below to calculate the observed t-score for the independent groups t-test. **Report your answer to four decimal places. Frequent Praise Praise at the End 8 2 5 3 2 8 3 8 6 6 4 7 7 6

2i. What is the 95% confidence interval for the problem? **Report both values to four decimal places. [lower] to [upper]