For each of the five research scenarios listed below:a. Identify the key independent variable (IV) and dependent variable (DV) in each scenario.  (0.5 mark)b. Construct a directional hypothesis of the relationship between these variables for each of your scenarios.  (0.5 mark)

 

Research Scenarios 1. Scenario 1:  Suppose that you want to conduct a study to see if the number of friends a person has is associated with the person’s level of self-esteem. The research is based on a theory that having friends improves self-esteem.
IV: DV: Hypothesis:
2. Scenario 2:  A researcher was interested in the relationship between number of employees supervised and the resulting managers’ anxiety levels.  He asked five managers to fill out an           anxiety questionnaire and took note of how many employees were under their supervision.
IV: DV: Hypothesis:
3. Scenario 3:  Parents of prep-aged children were asked to complete a questionnaire about their child’s experiences in child care and prep.  The researcher conducting the study was             interested in the relationship between the number of days per week the child went to pre- school/child-care in the year prior to them starting school and the child’s confidence levels              entering Year 1.
IV: DV: Hypothesis:
Continue on the next page.

4. Scenario 4:  A researcher was interested in how frequency of exercise per week is related to depression levels. The research is based on a theory that exercise reduces depression levels.
IV: DV: Hypothesis:
5. Scenario 5:  A researcher is testing a theory that suggests that managerial motivation increases with age. To test this theory, she measures managerial motivation and records each           participant’s age.
IV: DV: Hypothesis:

 

 

. For your chosen two variables:a) Construct a directional hypothesis about the relationship you expect to find between these 2 variables.  (0.5 mark)

 

b) Identify which variable is your independent variable (IV) and which is your dependent variable (DV). (0.5 mark)
IV:DV:
2. For each of your two variables:a) Please list the raw scores on each variable paired for every participant.
Participant IV DV1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Continue on the next page. b) Create a frequency table (0.5 mark)
If you can insert a computer-generated table here, you are welcome to do so.If you prefer to draw this table by hand, insert an image of your hand-drawn table here (see assignment guidelines for detailed instructions).

 

 

 

 

 

 

 

c) Create a histogram (0.5 mark)
If you can insert a computer-generated histogram here, you are welcome to do so.If you prefer to draw this histogram by hand, insert an image of your hand-drawn histogram here (see assignment guidelines for detailed instructions).

 

 

 

 

 

Continue on the next page.
3. For each of your two variables, calculate the following:a) Mode (0.5 mark)

b) Median (0.5 mark)

c) Minimum and maximum score (0.5 mark)
Minimum:Maximum:
d) Range (0.5 mark)

e) Mean (1 mark)

f) Standard deviation (1 marks)

4. Based on visual inspections of your histograms as well as the central tendency statistics you have calculated, determine whether the distributions of your two variables are symmetrical or skewed and explain your decision. (1 marks)

 

 

Continue on the next page. 5. From the data you have collected on the two variablesa) Construct a correctly formatted and labelled scatterplot. (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).

 

 

 

 

 

 

 

 

b) Based on a visual inspection of the scatterplot, give an estimate (in words, not numbers) of the strength and direction of the relationship between your variables. Then explain how this estimate relates to your hypothesis about the relationship you expected to find between these two variables.  (2 marks)

 

 

Theory suggests that fantasy proneness (having very strong imaginative tendencies, vivid daydreams and a tendency to have difficulty distinguishing between the real world and fantasised experiences) is strongly related to hypnotisability (the ease with which a hypnotic state can be induced in a person). To investigate this theorised relationship, a researcher asked 10 participants to complete a fantasy proneness questionnaire (with scores ranging from 1 to 30) and attempted to hypnotise each participant.  The researcher then rated each participant on a scale of 1 to 10, where 1 indicated that the participant was completely un-hypnotisable and 10 indicated the participant was highly hypnotisable (i.e. fell quickly into a deep trance state).  The data collected by the researcher are presented in the calculations table below. Fantasy Proneness: M = 10.70; SD = 6.02Hypnotisability: M = 5.20; SD = 2.09Fantasy Proneness (X) X-M Z x Hypnotisability (Y) Y-M Zy (ZX)(ZY)12.00 5.00  19.00 9.00  15.00 4.00  8.00 7.00  2.00 5.00  10.00 2.00  22.00 8.00  8.00 3.00  6.00 4.00  5.00 5.00
1. Based on this study and data:a) Give a directional hypothesis explaining the nature of the hypothesised relationship clearly indicating what is the predictor and the criterion variables. (1 mark)

 

Continue on the next page. b) 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).

 

 

 

 

 

 

 

 

 

c) Based on a 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. Please calculate the following statistics (a and b). For each statistic, give its value and the formula you have used for computing it. Then explain the meaning of the value of the statistic in terms of the relationship between the variables (c). Hint: start by filling in the table on page 9.
If you can insert a computer-generated formula in the appropriate section of each question below (a and b), you are welcome to do so.If you prefer to write these formulas by hand, insert an image of your hand-written formula below (see assignment guidelines for detailed instructions).

Continue on the next page. 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) Calculate the Correlation Coefficient (2 marks)
Value of statistic:
Formula used:
b) Calculate the Coefficient of Determination/proportionate reduction in error (0.5 mark)
Value of statistic:
Formula used:
c) Construct a statement about the theorised relationship between the variables using these statistics to support your statement (2 marks)

3. Another researcher conducted a different study that examined the relationship between observed hypnotisability (as rated by the researcher), and the self-reported scepticism towards hypnotism as measured via a questionnaire.  Scores on hypnotisability ranged from 1 to 10 with higher scores indicating higher hypnotisability.  Scores on scepticism ranged from 1 to 20 with higher scores indicating greater scepticism towards hypnosis.  This researcher collected data from 20 participants and calculated the following correlation and regression statistics.    r = – 0.40, r2 = 0.16a) Explain the strength and direction of the relationship between these two variables (1 mark)
b) How much variation in hypnotisability scores can be explained by scepticism towards hypnosis? (0.5 mark)
c) If r = -0.80 rather than -0.40, by how much would the percentage of variance in hypnotisability scores explained by scepticism increase? (1 mark)

 

End of Section C. Section D:  Relative Standing and Probability (15 marks in total)The table below presents the means and standard deviations of Year 3 students on a standardised maths test in a single primary school, as well as all Year 3 students in Queensland primary schools and all Year 3 students in Australian primary schools.  Scores on this test can range from 0 to 35 marks.  (Note: to answer some of these questions you will need to refer to Normal Curve Table A-1 in the appendix of your text)Population Mean of Maths Test Scores Standard Deviation of Maths Test ScoresYear 3 students at Green Hills Primary School 23.50 3.50Year 3 students at Blue Lake Primary School 17.50 3.30Year 3 students in Queensland Primary Schools 22.00 4.50Year 3 students in Australian Primary Schools 24.20 5.00Note.  These population parameters are fictitious.1. Please answer the following questions about Yusef who is a Year 3 student at Green Hills primary school.  He scored 25 out of 35 on the maths test.  a) Calculate his Z score in relation to the other Year 3 students at his school and explain what this Z score tells you about his relative standing among his peers at school. (2 marks)
Z =
What this Z score tells you:

b) Calculate his Z score in relation to other Year 3 students across Queensland and explain what this Z score tells you about his relative standing among his peers across the state. (2 marks)
Z =
What this Z score tells you:

c) Calculate his Z score in relation to other Year 3 students across Australia and explain what this Z score tells you about his relative standing among his peers across the country.  (2 marks)
Z =
What this Z score tells you:

Continue on the next page. d) Is Yusef’s position better within his school, state or country-wide cohort? Explain your reasoning. (1 marks)

 

2. Please answer the following questions about Maria who is a Year 3 student at Blue Lake Primary School.  Her teacher is very proud of her as she obtained a Z score of 2.5 when compared to the other Year 3 students at her school.  a) Where would Maria be placed within the school cohort if she were a student at Green Hills Primary School? Explain your reasoning. (2 marks)

 

b) What would Maria’s raw score for the maths test be if she was placed at the 90th percentile of Year 3 students in all Australian Primary Schools? (2 marks)

 

3. Please use the normal curve table to answer the following questions based on the information given in the table above. a) Between what scores on the maths test did the middle 50% of Year 3 Queensland Primary School students score? (2 marks)

 

b) What is the probability of scoring above 25 on the maths tests for a student at Green Hills Primary School (1 mark)

 

c) What is the probability of scoring above 25 on the maths tests for a student at Blue Lake Primary School (1 mark)