STA101: Business Statistics- Central Tendency & Spread- Report Writing Assignment

Report Writing Assignment:

Task: This assignment is about data on quiz scores etc. at a college. Answer all the questions. Keep your workings brief and to the point. Round all final numerical answers to two decimal places or whole numbers, depending on your judgement. Interpret your numerical answers; explain what they mean. Use MS Excel to sort data and to do your calculations. For formulae, use MS Word’s equation function. Craft a report. Imagine that you are to deliver it to your client, the college. Base it on your workings, answers and interpretations. Divide the report into the appropriate sections (e.g., ‘1. Introduction’, ‘2. Central tendency and spread’, ‘3. z-scores’, ‘4. Chi-squared test’…). Do not copy the questions into your report. Follow the instructions and marking criteria on Moodle ? Assessments ? Individual assignment template. You are to investigate student performance in a dreaded statistics course at Collage College. The college has commissioned you, a consultant, to advise them about it. Pretend that you collected a random sample of 94 students from a pool of students who had done that statistics course last year. You recorded their quiz scores and other data. The assumptions: (i) This is a randomly selected sample of students that is representative of the population you are investigating (ii) The quiz scores and other continuous data are normally distributed The population: All students who completed a statistics course at a college last year The goal: (i) To describe the data in the sample (ii) To make inferences about all the statistics students at that college last year The data: Quiz scores and other data selected over the course of last year. Available from: Moodle ? Assessments ? Individual assignment: the questions ? Data dossier Start the report with a simple introduction. The framework of the questions will help you structure the report. No conclusion section is needed at the end of the report; each section has its own conclusions (your interpretations). Section A: Descriptive statistics Central tendency and spread 1. What’s the mean, median, mode, and standard deviation for the quiz scores in the sample? Is it skewed? z-scores 2. What is the z-score for the highest score in the sample? What is the z-score for the lowest score in the sample Which of these do you deem significantly different from the mean (unusually low or high)? Why? Section B: Inferential statistics Chi-squared test 3. For the population, is there evidence of a connection between student gender (male or female) and whether they obtained ‘top grades’ (namely, high distinctions (HD) and distinctions (D)) or ‘other grades’ (credits (C), passes (P) or fails (F))? 4. For the population, is there evidence that whether a student attempts quizzes in the day or at night depends on gender? For each question: (i) state the null and alternative hypotheses (ii) show the expected values, ? 2 differences, and the total and critical ? 2 values [2 marks] (iii) interpret your results [2 marks] The normal distribution 5. If the data and its distribution reflect the population, what proportion of students in an academic year do you estimate might have: (i) passed the course (50% or higher)? (ii) failed (iii) obtained a distinction (between 75% and 85%)? 6. To be in the top 5% of students that year in terms, what minimum score must a student get (in %)? Hypothesis testing I (with one sample) 7. In the years prior to last year, students were known to score approximately 60% on average for their quizzes. The college expects quiz results last year to be significantly higher than the results from previous years. That’s because they hired a more expensive lecturer. Based on your data, do you have evidence that the mean quiz score last year is significantly higher? For this question, state: (i) the null and alternative hypotheses (ii) the significance level used (iii) the critical t-score (iv) the calculated t-score (v) the decision made regarding the hypotheses (vi) Your interpretation of the results Hypothesis testing II (using two samples) 8. Is there a significant difference in the population between domestic and international students when it comes to the duration taken to complete quizzes (in minutes)? Report, for each question: (i) the null and alternative hypotheses (ii) the significance level used (iii) the critical t-score (iv) the calculated t-score (v) the decision made regarding the hypotheses (vi) Your interpretation of the results