Question

Q1. Hypothesis testing using a Z test (14 points)

A professor has been teaching introductory statistics for many years and the final exam performance (30 points total) has been very consistent from class to class and the scores have been normally distributed. Overall, the whole data base (i.e. population) of final exam scores has a mean (μ) of 20 points and a standard deviation (σ) of 5 points. Because 20 out of 30 is only about 67%, the professor would like to try a new format to see if student performance could be improved.

So in the most recent class, students were allowed to make two attempts (instead of one attempt) at the final exam. There were 64 students and the class average on the final exam was 21.5. The professor would like to run a hypothesis test to see if this sample of students (with two attempts) performed significantly better than the past population (with one attempt). In other words, the hypothesis was a comparison between the population of one attempt and the population of two attempts (represented by the sample of 64 students).

The professor is predicting an increase of final exam score with two attempts, so the hypotheses should be directional, and the test should be one-tailed. α = .05.

a. Identify the dependent variable for this study (1 point)

b. Hypothesis testing is always about making inferences about the populations. The recent class of 64 is considered a sample. What is the population from which this sample has been drawn? (1 point)

c. State your null hypothesis and alternative hypothesis using both words and symbol notation

Note: The hypotheses should be directional.

(2 points total. Each hypothesis is 1 point, with .5 for the written and .5 for the notation)

d. Calculate standard error (SE, which is the standard deviation of the sampling distribution) (2 points total: 1 if the process is correct but the result was calculated incorrectly)

e. Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) (2 points total: 1 if the process is correct but the result was calculated incorrectly)

f. Determine the critical value for Z. Explain how you come up with the answer. (1 point: .5 for the answer and .5 for the rationale)

g. Compare the Z statistic with the critical Z value (that is, “is the Z statistic more extreme than the critical Z?”), and then draw a conclusion about the result of the hypothesis test (do you “reject” or “fail to reject” the null hypothesis?) (2 points: 1 for Z statistic comparison; 1 for hypothesis test decision)

h. Write 1-2 sentences to answer the research question (you can use the wording from the hypotheses or explain it in another way) (1 point)

i. Calculate the standardized effect size for this test. (2 points total: 1 if the process is correct but the result was calculated incorrectly)

Answer 1