i.  Review ‘Late submission’ and ‘Academic integrity’ in the ECMT1010 unit outline.

ii.  Enter your answers using the Word template.

iii.  Save your answers as a PDF file named after your 9-digit Student ID (SID), e.g., 567891234.PDF. Do not include your name or a cover sheet.

iv.  Submit the PDF of your answers under ‘Assignment’ on Canvas. Work submitted after 11. 59PM Sunday 2 November 2025 is subject to a penalty of 5% per calendar day late. Work submitted after 11. 59PM Wednesday 12 November 2025 will receive a mark of 0.

v.  Use your assigned data set (see below).  Enter your data set number using the box provided in the Word template. Use of the wrong data set may be reported to the Educational Integrity Coordinator, Faculty of Arts and Social Sciences. Use of the wrong data set will result in low marks (because most of your answers will be wrong).

vi. There are 10 questions worth 2 marks each for a maximum of 20 marks.  Answer all questions. The assignment is anonymously graded (provided you don’t put your name on it).

vii.  Show numerical answers to 3 decimal places.  Carry out all tests at a 5% level of significance.

viii. When communicating statistical results, it is important to be accurate and concise. Keep your comments, conclusions, comparisons, etc., to one or two sentences. Ex-cessively long responses indicate a lack of understanding and will be penalised ac-cordingly.

Aim: The assignment illustrates the use of various statistical methods and software (e.g., Excel, StatKey) to analyze economic data.

Data description: Your assigned data set is extracted from the Student Survey dataset in the 2nd edition of the Lock et al. textbook. It consists of information on Scholastic Assessment Test (SAT) score, grade point average (GPA), and body piercings from a randomly-selected sample of 36 undergraduate students at a U.S. university.

•  You must use the data set assigned to you, which is determined by the last digit of your Student ID (SID). For example, if your SID is 567891234, you must use the dataset Students4.xlsx.

•  The first row contains the variable names; the remaining 36 rows contain the infor-mation for each of the 36 students in your sample.  The column heading Obs iden-tifies each student (and can be ignored), SAT is each student’s combined SAT score (required for entry into many U.S. universities), GPA is the student’s grade point av-erage (a measure of overall academic performance), Piercings denotes whether the student has a body piercing (0 = none, 1 = at least one piercing).

QUESTIONS

1.  You are curious whether, in terms of GPA, students with body piercings perform worse than students without any piercing, on average. Define your notation clearly and set up the appropriate null and alternative hypotheses.  [2 marks]

2.  Using Statkey with the ‘reallocate groups’ randomization method, produce a dotplot of the randomization distribution (with 5,000 samples) of the appropriate sample statis- tic.  Carry out the hypothesis test using the randomization distribution and state your conclusion.  [2 marks]

3.  Produce a scatterplot of GPA against SAT score using your sample. Compute the sample correlation and comment on the degree of association between the two variables. (There is no need to show any computational steps.)  [2 marks]

4.  Write down the null and alternative hypothesis to test whether there is a linear associ- ation between GPA and SAT score.  Define your notation and clearly show the null and alternative hypothesis.  [2 marks]

5.  Test whether there is a statistically significant linear association between GPA and SAT score. Show your steps and state your conclusion.  [2 marks]

6.  To further investigate whether GPA is a linear function of SAT score, you decide to set up an appropriate regression model. Write down your regression model taking care to define your notation clearly. Estimate the regression model and report your results.  [2 marks]

7.  Use your regression results to give a one-sentence interpretation of the regression slope estimate.  [2 marks]