CONFIDENCE INTERVALS
For the confidence intervals, you will be using the PANIC process. You MUST include the following to earn full credit:
P: State the random variable AND the parameter in words, using correct statistical notation
A: Check the assumptions for approximate normality for the sampling distribution of quantitative data
N: The “Test” you are using on your calculator, AND the values you are entering into the calculator for that test.
I: Name the point estimate AND give the confidence interval in interval form
C: State your final conclusion in words in the context of the problem.
Using the PANIC process, construct a 90% confidence interval for the GPA of students who record, on average, LESS than 10,000 steps per day.
Using the PANIC process, construct a 90% confidence interval for the GPA of students who record, on average, MORE than 10,000 steps per day.
What do the two confidence intervals tell you about the data? Can you reach any conclusions about a difference between the two groups (those who logged on average less than 10,000 step per day, and those who logged more than 10,000 steps per day) based on the confidence intervals?
HYPOTHESIS TESTS
Oral Roberts University has a “Fast Track” program that allows upper-level (junior and senior) students to enroll concurrently in both undergraduate and graduate courses. Students must have maintained a minimum GPA of 3.00 to be considered for this program. Even though the students in our sample are only First-year students, we will use a GPA of 3.00 as our benchmark grade. For our first hypothesis test, we will be testing the claim that students who average less than 10,000 steps per day have an average GPA of more than 3.00. For our second hypothesis test, we will be testing the claim that students who average more than 10,000 steps per day have an average GPA of more than 3.00.
For the Hypothesis tests, you do NOT have to use the full PHANTOMS process, since you have already completed some of the steps with your confidence interval. However, you MUST include the following:
H: The null and alternative hypothesis (using correct notation)
N: The “Test” you are using on your calculator, AND the values you are entering into the calculator for that test.
T: The sample statistic and the test statistic (using appropriate statistical notation for each)
O: The p-value (again, using appropriate statistical notation)
M: Whether you reject or fail to reject the null hypothesis
S: Your final conclusion in the context of the problem.
Test the hypothesis that students who record, on average, LESS than 10,000 steps per day will have an average GPA greater than 3.00. Use a 5% level of significance.
Test the hypothesis that students who record, on average, MORE than 10,000 steps per day will have an average GPA greater than 3.00. Use a 5% level of significance.
Based on the conclusions of each of the hypothesis tests, can you make any conclusions about the academic achievement of each of these groups? Clearly explain your reasoning.
CONCLUSION
Return to the original article. Re-read the discussion and the Conclusion on pages 10-11. Summarize the findings of YOUR statistical analysis of the sample data by answering the following questions. Be sure to address ALL of the points below, plus anything else you think is relevant to your conclusions.
What connections do you see between the DESCRIPTIVE statistics (your boxplots & histograms) and the INFERENTIAL statistics (your confidence intervals & hypothesis tests). Be specific.
