statistics question to help me learn
Section A: Variable Recognition and Hypothesis Development (3 marks in total) For each of the two research scenarios listed below: a. Identify the key independent variable (IV) and dependent variable (DV) in each scenario. (0.5 marks) b. State whether the IV is within- or between-participant. (0.5 marks) c. Construct a directional hypothesis of the relationship between these variables for each of the scenarios. (0.5 marks) Example Research Scenario A researcher conducts a study to see if the number of friends a person has is associated with the person’s level of self-confidence. The research is based on a theory that having friends is a cause of self-confidence. The researcher asks each participant how many friends they have and also measures each participant’s level of self-confidence using a questionnaire. IV: Number of Friends DV: Level of self-confidence IV type: Between-participant Hypothesis: People who have more friends have higher levels of self-confidence. Research Scenario 1 A human factors researcher was interested in whether listening to music or talk shows on the radio while driving would differentially affect driving behaviour. The researcher identified a sample of 50 drivers who always listened to music and another sample of 50 drivers who always listened to talk shows, and monitored how many times each driver exceeded speed limits during a one-month period. The researcher suspected that talk shows might be more distracting than music, making drivers pay less attention to driving. IV: DV: IV type: Hypothesis: Research Scenario 2 A pharmacologist claimed she developed a new drug that would enhance people’s ability to study complex information. However, sceptics did not believe her claim. In an attempt to demonstrate the effect of the drug, the pharmacologist recorded students’ midterm exam scores, and gave them the drug before they took the final exam. The pharmacologist recorded the same students’ final exam scores too. The pharmacologist compared the students’ midterm and final exam scores (i.e., before and after taking the drug). IV: DV: IV type: Hypothesis: Section B: Data Display, Central Tendency, and Variability (7 marks in total) In this section, you will be analysing data from a mock survey of students. Use section B data to analyse. Your task is to perform a range of descriptive statistical tasks on these data. You must use only the data that have been specifically provided. Participant Number 1 Interest in Psychology Private Practice Score 14 2 14 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 14 16 16 15 15 15 16 14 20 15 14 10 15 15 13 17 16 18 17 15 15 10 14 To do the survey, 25 students were randomly sampled and they were asked to rate their levels of interest, in the scale of 0–20, in having their own private practice as a psychologist in the future (0 being not interested at all; 20 being very much interested). In this section, you do not need to show your workings, but please ensure you check all your workings very carefully as an error in an earlier question may lead to an error in subsequent questions. 1. Create a frequency table for your data (0.5 marks) If you can insert a computer-generated table here, you are welcome to do so. If you prefer to draw the table by hand, insert an image of your hand-drawn table here (see assignment guidelines for detailed instructions). Continue to the next page. 2. Create a histogram for your data (0.5 marks) If you can insert a computer-generated histogram here, you are welcome to do so. If you prefer to draw the histogram by hand, insert an image of your hand-drawn histogram here (see assignment guidelines for detailed instructions). Continue to the next page. 3. Using your data, calculate the following: a) Mode (1 mark) b) Median (1 mark) c) Range (1 mark) d) Mean (1 mark) e) Sum of squares (1 mark) 4. Based on visual inspection of your histogram as well as the central tendency statistics you have calculated, determine whether the distribution of your data is symmetrical or skewed, and explain your decision. (1 mark) End of Section B. Section C: Correlation (10 marks in total) Theory suggests that overuse of the social media may be detrimental to people’s self-esteem because they can do too much of upward comparison against other people who seem to be better off. To test this theory, a social psychologist surveyed 10 university students and recorded how many hours per week they spent online for browsing social media posts, and also gave them a questionnaire that measured their sense of self-worthiness. The data collected by the social psychologist is presented in the calculations table below. Time spent on the social media per week was measured in hours. Students’ sense of self-worthiness was measured in scores that could range from 0 to 100 (higher scores indicate greater sense of self-worthiness). Time on social media (X) X −M ZX Self-worthiness (Y) 21 92 32 93 25 63 49 7 31 88 23 58 35 62 32 16 32 50 26 77 Continue to the next page. Y −M ZY (ZX)(ZY) 1. Based on this study and data: a) Construct a correctly formatted and labelled scatterplot of the data. (1 mark) If you can insert a computer-generated scatterplot here, you are welcome to do so. If you prefer to draw this scatterplot by hand, insert an image of your hand-drawn scatterplot here (see assignment guidelines for detailed instructions). Continue to the next page. b) Based on visual inspection of the scatterplot, give an estimate (in words, not numbers) of the strength and direction of the relationship between the variables (e.g., no relationship; strong positive relationship). (1 mark) 2. Using the above data, calculate the following: You do not need to show your workings, but please ensure you check all your workings very carefully as an error in an earlier question may lead to an error in subsequent questions. a) ΣZXZY (2 marks) b) Correlation coefficient (0.5 marks) c) Coefficient of determination (proportionate reduction in error) (0.5 marks) 3. Using the coefficient of determination calculated above, explain how much variation in the selfworthiness scores can be explained by the social media use. (1 mark) 4. Explain what the data tell about the theorised relationship between the variables. Support your explanation using the correlation coefficient and the coefficient of determination calculated above. (2 marks) 5. Suppose that the social psychologist collected new data from another group of students and found r = −0.33 and ΣZXZY = −9.9. How many students did the social psychologist have in this new sample? (2 marks) End of Section C. Section D: Relative Standing and Probability (10 marks in total) The table below presents results from a fictitious survey, which asked students how enjoyable their study was at the University of Brisbane. The students rated their experience in the scale of 0 to 100, 0 being not enjoyable at all and 100 being very much enjoyable. Means and standard deviations of the students’ scores were calculated for each course of study within the Faculty of Arts and Sciences, for the entire Faculty, and for the entire university. Use these data to answer questions below. To answer some of the questions in this section, you will need to refer to the normal curve (Z score) table (Table A-1 in the appendix of your prescribed text; its copy is also available on the unit’s Blackboard site). Mean of survey scores Standard deviation of survey scores Students studying mathematics 76 15 Students studying English literature 82 22 All students within the Faculty of Arts & Sciences 70 31 All students at the University of Brisbane 80 10 Population Note. These data are fictitious. 1. Answer the following questions about Valentina who majors in mathematics. Her score on the survey was 85. a) Calculate her Z score in relation to the other mathematics students at the University of Brisbane and explain what this Z score tells you about her relative standing among her fellow maths majors with regard to how happy she was about her study. (2 marks) Z= What this Z score tells you: b) Calculate her Z score in relation to all the other students within the Faculty of Arts and Sciences and explain what this Z score tells you about her relative standing among her peers across the Faculty with regard to how happy she was about her study. (2 marks) Z= What this Z score tells you: Continue to the next page. c) Compare Valentina against other maths majors, students majoring in other subjects within the Faculty of Arts and Sciences, and all students at the University of Brisbane. In which comparison is Valentina happiest relative to the other students within each group? Explain your reasoning. (2 marks) 2. Wei majors in English literature. In the survey, he was placed at the 91st percentile of all students at the University of Brisbane. Where was Wei placed within English literature majors? Explain your reasoning. (2 marks) 3. If you look at the middle 60% of the distribution of survey scores given by students in the Faculty of Arts and Sciences, what raw scores will you find at the lowest and highest ends of this portion of the distribution? (1 mark) 4. What is the probability of giving 70 or below on the survey for a student who majors in mathematics? (1 mark) End of Section D. End of this document.
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