Submission via Turnitin
Part A. Multiple Choice Questions (5 points, 1 point each question)
A1. When we conduct a t-test, we have to be cautious about the structure of our data.
Which is the following is not a concern?
A) single sample vs. paired groups
B) correlated groups
C) independent groups
D) mutually exclusive groups
A2. For a simple linear regression with two variables X and Y, we can estimate the slope in the linear regression line by Pearson correlation r between X and Y, and the standard deviation of SX and SY. If we know r = 0.75, SX = 5, and SY = 8, what is the estimated slope (b) of the line Y = a + bX?
A) 3.75
B) 0.469
C) 1.2
D) 1.6
A3. In linear regression, if we know Y = 25+ 1.3 X. Given a change in the independent variable X of 20 units, what is the corresponding change in the dependent variable Y?
A) 51 units
B) 26 units
C) 25 units
D) 1.3 units
A4. Power of test could be affected by a few factors, what of the following is NOT one of them?
A) sample size N
B) sample variability S
C) confidence interval
D) the size of the real effect of the independent variable
A5. If two samples are selected from the same population, under what circumstances will the two samples have exactly the same t statistic?
A) If the sample size (n) is the same for both samples.
B) If the samples are the same size and have the same mean.
C) If the samples are the same size and have the same mean and have the same sample variance.
D) None of the other options are correct.
Part B. Short Essay Questions. Please use hand calculation to show the steps. (20 points total)
B1. A nutrition store in the mall is selling Memory Booster which is a concoction of chicken essence, herbs and minerals that is intended to improve memory performance. To test the effectiveness of the Memory Booster, a researcher obtained a sample of n = 30 participants and divided them into two groups with equal sample size. In one group, the researcher asked each participant to take the suggested dosage each day for 4 weeks. In the other group, the participants did NOT take any of the Memory Boost. At the end of the four-week period, each individual took a standardized memory test. The scores from the Memory Boost sample produced a mean of M1 = 26 with SS = 960. In the group that did not take the Memory Boost, the mean is M2 = 20 and SS = 1100.
a. Do the sample data support the conclusion that the Memory Booster has a significant
effect? Test with α = .05. (5 points)
b. Compute effect size of the Memory Boost. (3 points) Locate the critical region:
df1 = 15-1 = 14, df2 = 15-1 = 14
Since SS1 = 960 and SS2 = 1100,
๐2= (960 + 1100)/ (14+ 14) = 73.5714
Cohen’s d = 26−20
√73.5714
= 0.6995 = 0.70 (2. ๐. ๐)
The effect size is 0.70 standard deviation units. Memory boost has a medium effect on improving memory performance
c. What is your conclusion of the study? (2 points)
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