**P****SYCHOLOGY**** 315, Winter 2018, Practice L****AB**** T****EST**** II**

**______________________________________ ______________________________________**

**Name Student Number**

**Please note. You are not permitted to use worksheets developed in previous labs. All work must be done in the Excel workbook that you download from Moodle.**

Answer all questions in this test in the space provided. **Please give all numerical answers to exactly five (5) decimal places. Marks will be deducted if your answers have more or fewer than five (5) decimal places.**

**Part A. (6 Marks) **An experimenter would like to test the effects of sleep deprivation on maze learning in lab rats. It is known that without sleep deprivation, rats take µ = 10 trials on average to learn a maze with σ = 3.423. Previous work suggests that sleep deprivation will lead to longer maze solving times, and the improvement is associated with an effect size of 0.135. The experimenter would like to conduct a one-tailed z test with α = .05. How many participants, __rounded up__, would be required to achieve power = .95. Show the following quantities for the required sample size.

- β __________.05____________ [1 marks]
- δ __________.135____________ [1 marks]
*n*__________593 ± 2____________ [4 marks]

* *

**Part B. (12 Marks)** The data for Part B are found in the Sheet 1 of the **Lab Test 2** workbook under the heading

**Part B Data**. These data represent final grades on a Neurobiology exam written on the last day of the final exam period.

- Calculate the 75% and the 95% confidence intervals around the mean of these grades.

- 75% CI = _____________ [53.55331, 55.94192] ___________________ [2 marks]

- 95% CI = ____________ [52.70660, 56.78864] _________ [2 marks]

- It is known that when the exam is written on the first day of exams the average grade is μ
_{0}= 57.093. A researcher wonders whether it makes a difference if the final exam is written on the first or last day of the exam period. State*H*_{0}and*H*_{1}__in symbols.__

*H*_{0}________ H0: μ1 = μ0__or__μ1 – μ0 = 0 ______________ [1 mark]

*H*_{1}________ H1: μ1 ≠ μ0__or__μ1 – μ0 ≠ 0 ______________ [1 mark]

- Based on the confidence interval calculated in 1.b, and assuming α = .05, explain why we should we retain or reject the null hypothesis. [2 marks]

The 95% CI computed in 1.b does not capture μ0 so we can reject H0.

- Calculate the estimated effect size from the mean of this sample (
*m*) and the population mean (μ_{0}), and calculate the approximate 95% confidence interval around this estimate.

- Estimated effect size = ________ -0.156324 [2 marks]

- 95% confidence interval = _________ [-0.29241, -0.02024] [2 marks]

# Part C. (6 Marks)

**1**. [2 marks] If 12% of a t-distribution lies outside the interval ±t when n = 21, what is t? t = ______ 62415 _______- [2 marks] What proportion of a t-distribution lies below 2.18, when sample size is 81? p = _____ 0.98390 ______
- [2 marks] If 24.5% of a t-distribution with 81 df lies within the interval ±t, what is t? t = ______ 0.31311 _______

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**Part D. (11 Marks) **Bargh, Chen, and Burrows (1996) predicted that exposure to words associated with old age and fragility would have a subconscious effect on people and cause them to walk more slowly than the average walking speed. The average person walks μ_{0} = 3.45323 km/h. In their experiment, Bargh et al. brought 42 participants to a research lab and asked them to solve word problems. The group of participants solved problems involving words such as old, bingo, and Florida. Unknown to the participants, the researchers measured their walking speeds when they left the research lab. The dependent variable was walking speed, measured in kilometers per hour. The results of this study can be found in the Sheet 1 of the **Lab Test 2** workbook under the heading **Part D Data**.

- State
*H*0 and*H*1 in symbols*H*_{0}______ μ1 = μ0__or__μ1 – μ0 = 0 ______ [1 mark]*H*_{1}______ μ1 ˂ μ0__or__μ1 – μ0 ˂ 0 ______ [1 mark]

- Determine the critical value of the
*t*-statistic required to reject*H*_{0 }, assuming α = .01.___ -2.42080___ [1 mark] - Show the formula for the statistic you will use to test
*H*_{0}: ___________ t_{obs}= (m – μ_{0})/s_{m }___________ [1 mark] - Use the formula from part 3 to compute the statistic. ___________ -11.77526 ___________ [2 marks]
- Should you retain or reject
*H*_{0 }?! _________ REJECT!!! t_{obs}is ˂ t_{critical}___________ [1 mark] - Calculate the estimated effect size of the difference between the sample mean and the population mean, and calculate the approximate 95% confidence interval around this estimate.
- Estimated effect size _________ -1.81696 _________ [2 marks]
- 95% confidence interval = _________ [-2.31308, -1.32085] _________ [2 marks]