Submit a typed, neat and organized final paper that shows each solution/answer in order. This should look like a professional report in quality of presentation. Please do not include a cover page. To ensure blind review, do not include your name. Use just your student ID number, along with the course and section number, as a header at the top of the first page. Please open this document in Word and use it as the template for your report. Prior to submission on Blackboard, however, you should save the document as a PDF (or print to PDF).
Parts of problems (1.a-f and 2.a-d) and steps within hypothesis tests should be clearly labeled and highlighted on your submitted assignment. These labels should be at the edge of the left margin, with everything else indented, so as to visually set apart the labels (as in an outline). This Word document is already set up that way; please use it as a template in which to complete the assignment. Do not attach appendices showing your calculations, but rather show your calculations/demonstrations ahead of each solution, in order.
Keep at least two decimal places during calculations.
Show your work. When using formulas, copy the formula, substitute the values, show samples of any individual calculations you did, and then provide the answer. The formulas included in this document are editable. You can copy and paste them where you need them, or move them, then use the equation editor to add onto them. When a formula requires repetitive calculations, first provide a demonstration of the use of the formula. In this, you may show the first of the calculations by hand, write “…”, and then show the last of the calculations as your demonstration for use of formula. In addition present a table or copy-paste a spreadsheet to show all of the individual calculations. For a model of this, please see worksheet solutions documents posted in Blackboard under the relevant topics.
Your grade on the assignment will reflect whether you followed these instructions. See rubric at end.
1. A statistics instructor is curious to find out if an assignment designed to help students apply concepts ahead of an exam is effective. As a first pass at testing this question, the researcher tested the relationship between assignment and exam performance by collecting data from 30 students on assignment (AP) and exam scores over the course of a semester. The data are included in an Excel file called “AP3 dataset”.
a) (2 pt) Draw (or generate in Excel) a scatterplot of the data with labeled axes. The plot should be large and precise, so every individual point is easily discernable.
b) (7 pt) Conduct a hypothesis test (significance level 0.05) to see if there is a significant positive relationship between AP scores and exam scores. A list of useful formulas is provided below.
c) (2 pt) Write up the results of the study in one sentence as it would appear in a publication (being sure your conclusion respects the limitations of the methodology used). At the end of the sentence, in brackets, report your test statistics and p-value.
d) (1 pt) Calculate and report (in a sentence) the proportion of variance in these two measures you have explained through their relationship with each other.
e) (2 pt) Calculate and report the equation for the best fit regression line for these data. Also, reproduce the scatterplot you created for part a, and plot the regression line precisely on this new copy of the scatterplot.
f) (2 pt) Predict the exam score for an individual with an AP score of 50. Report the actual exam scores(s) for individual(s) with an AP score of 50. Comment on why the actual exam score(s) is/are not the same as your prediction.
2. The same investigator decided to analyze the data differently, dividing up the participants into Low, Medium, and High AP-score groups. In other words, you will convert AP score from a numeric to a nominal variable, leaving the exam score as the numeric variable for their analysis. (The dataset is already sorted by AP score, so the Low-AP group will include the first 10 participants, the Medium-AP group the next 10, and the High-AP group the last 10 participants listed.) You should now conduct statistical analyses to see if the mean exam score differs among these three groups.
a) (2 pt) Draw (or generate in Excel) a bar graph of the group exam-score means with labeled axes. Error bars are nice, but not necessary.
b) (7 pt) Conduct a hypothesis test that corresponds to this new analysis (significance level 0.05). Step 4 should conclude with a fully-filled-out summary table.
c) (2 pt) Write up the results of the study in one sentence as it would appear in a publication (being sure your conclusion respects the limitations of the methodology used). At the end of the sentence, in brackets, report your test statistic and p-value.
d) (4 pt) This new statistical design resembles one that might be used to analyze the results of an experiment. List the required features of experimental design that allow for causal conclusions. Then comment on whether it is appropriate to draw cause-effect conclusions from this analysis and why (or why not).
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