# MATHEMATICS

**Each of the six questions is worth 5 marks**

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**Question 1**

A researcher is evaluating the effectiveness of a new method of teaching statistics to University students. For the first year student population, statistics scores are known to form a normal distribution with a mean ofm = 70.00 and a standard deviation ofs = 16.00.

**a) **A random sample of *n*= 16 is selected from first year students. These students are given special tutorials for the first semester, and then given a statistics exam at the end of the semester. The average score for the sample is *M* = 76.00. Does the sample provide statistical evidence that the new method of teaching statistics is effective? Show your calculations and the logic of your response (e.g., what is the null hypothesis, critical values of statistics, etc.) **(2 marks)**

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**b) **Next year the researcher repeats the study but this time she is able to get a larger sample of *n* = 64. On this occasion, the sample mean following the teaching innovation is again *M* = 76.00. Do these data support the researcher’s claim that the new method of teaching statistics is effective? Show your calculations and the logic of your response. **(2 marks)**

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**c) **If there is a difference in the outcome of (a) and (b), how would you explain this. If there is not, why not? **(1 mark)**

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**Question 2**

A nutrition store in the mall is selling “Memory Booster” which is a concoction of herbs and minerals that is intended to improve memory performance. To test the effectiveness of the herbal mix (a= .05), a researcher obtains a sample of *n* = 16 people, and has each person take the suggested dosage each day for 4 weeks. At the end of the four-week period, each individual takes a standardised memory test. The scores from the sample produced a mean of *M* = 28.00 with a sample variance of *s ^{2}* = 64.00. In the general population, the standardized test is known to have a mean ofm= 20.00.

**a) **Do the sample data support the conclusion that the Memory Booster has an effect? Show your calculations and the logic of your response.** (3 marks)**

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**b) **Calculate a measure of the effect size. Briefly (in less than 100 words) state whether you would accept the store’s claim for the effectiveness of the memory booster, and if not, why not. **(2 marks)**

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**Question 3**

*You are to use SPSS to answer this question, however you may need to hand calculate the measure of effect size (show your formula and working out). *

Using the Attention Deficit Disorder data file (*ADD.sav*), investigate the following hypotheses using SPSS .a = .05, two-tailed.

i. There is a difference between boys and girls in symptoms of ADD.

ii. There is a difference between boys and girls in Grade Point average in ninth grade.

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**a) **Cut-and-paste your SPSS output into your report. **(1 mark)**

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**b) **Describe the results of these two hypothesis tests in a form that could go into the results section of a laboratory report. **(1 mark)**

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**c) **Discuss other information contained in your SPSS output that could help to interpret the outcome, for example the shape of the distribution of scores. **(1 mark)**

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**d) **Discuss whether it is likely that any assumptions have been violated. If this is the case, describe how seriously this might impact on the outcome of the analysis, and what strategies could be employed to minimize any such impact. **(2 marks)**

**Question 4**

A variety of research results suggest that visual images interfere with visual perception. In one study, Segal and Fusella (1970) had participants watch a screen, looking for brief presentations of a small blue arrow. On some trials, the participants were also asked to form a mental image. Data similar to Segal and Fusella’s results follow:

Participant |
Errors with Image |
Errors without Image |

A |
14 | 4 |

B |
9 | 2 |

C |
12 | 10 |

D |
7 | 8 |

E |
10 | 6 |

F |
8 | 6 |

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**a) **Does the formation of a mental image affect performance in this task? Show your calculations and the logic of your response. **(3 marks)**

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**b) **If Segal and Fusella had conducted this experiment so that the Image condition was first for all participants, what effect would this have had on the validity of their interpretation of the results. Describe two different procedures that could have been used to avoid this problem. **(2 marks)**

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**Question 5**

The data below are from a sample of students, completing an online test in statistics in Week 4 and Week 11 of Session.

Student | Week 4 | Week 11 |

1 | 4 | 6 |

2 | 8 | 7 |

3 | 7 | 8 |

4 | 2 | 5 |

5 | 6 | 7 |

6 | 6 | 6 |

7 | 4 | 6 |

8 | 5 | 8 |

Mean | 5.25 | 6.63 |

SD | 1.91 | 1.06 |

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**a) **Conduct an analysis to determine whether the students’ scores improve between Weeks 4 and 11 of session. If you do this by hand, Show your calculations and the logic of your response. If you use SPSS, cut-and-paste the output into your assignment. **(2 mark)**

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**b) **Imagine now that instead of testing the same students twice, the data had come from two separate groups of 8 students. Re-run your analysis if this had been the case. If you do this by hand, Show your calculations and the logic of your response. If you use SPSS, cut-and-paste the output into your assignment. **(2 mark)**

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**c) **Explain in a way that a non-expert in statistics could understand why there is a difference between these two outcomes. **(1 mark)**

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**Question 6**

You are talking to a friend, who has only just started to study psychology. They are having difficulty understanding a paper they have been asked to read. They show you the relevant section. It reads:

“There was a significant difference between the means for the S6+ group and the means for the S6+S5- group [*t*(26) = 2.01, *pt*(26) = 1.74,*pt*(26) = 3.73, *pt*(13) = 1.20, *p*> .05] or S6+S7- [*t*(13) = 0.10, *p*> .05] groups, but did differ significantly from the obtained means for the S6+S5- group [*t*(13) = 2.66, *p*

They ask you; “What do all these t’s and p’s and numbers in brackets mean? Why is the number in the brackets sometimes 26 and sometimes 13? What does it mean to say that there was a ‘significant’ difference?”

Explain null hypothesis testing to your friend in a way they might understand. Use diagrams if you think it might help. **(5 marks)**