8375a487-749e-44cc-a38c-2397df4e7323.pdf Submission via Turnitin Be as concise as possible. Total: 25 points Part A. Multiple Choice Questions (5 points, 1 point each question) A1. When we conduct...

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8375a487-749e-44cc-a38c-2397df4e7323.pdf Submission via Turnitin Be as concise as possible. Total: 25 points Part A. Multiple Choice Questions (5 points, 1 point each question) A1. When we conduct t-test, we have to be cautious about the structure of our data. Which in 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, ?? 2= (960 + 1100)/ (14+ 14) = 73.5714 Cohen's d = (X1 -X2) sp 2 Cohen’s d = 26−20 √73.5714 = 0.6995 = 0.70 (2. ?. ?) 21 2 2 21 2 1 21 212 dfdf dfsdfs dfdf SSSSsp 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) B2. Amy was interested in studying if third grade students’ math performance was related to their IQ. She then chose one of the schools in the community and conducted her study on the third grade students in a class. She first tested the students’ IQ and then looked into their most recent math test scores on a closed book exam. Here is the list of the scores she got. Student No. IQ score Math score 1 105 80 2 85 72 3 95 75 4 140 93 5 70 61 6 100 66 7 90 71 8 110 80 9 120 90 10 95 65 Please answer the following questions: a. Amy is interested in finding out if there is any correlation in the IQ and math score. Can you help her? What is the correlation? Is it significant? (5 marks) Yes, I can help her by using the Pearson’s correlation coefficient to solve this question. Pearson’s correlation coefficient will help me find out if there is any linear relationship (correlation) between the IQ score and math score. Step 1: Label the X and Y variables: Let the X-variable be IQ score Let the Y-variable be Math score Step 2: Find the mean values of X and Y To find the mean of IQ score (MX) : (105 + 85 + 95+ 140 + 70+ 100 + 90 + 110 +120 + 95) / 10 = 101 To find the mean of Math Score (MY) : (80 + 72 + 75 + 93 + 61 + 66 + 71 + 80 + 90 + 65) / 10 = 75.3 Step 3: Measure the variability of X and Y separately: SSX = ∑ (X - MX )2 = (105 - 101)2 + (85 - 101)2 + (95 - 101)2 + (140 - 101)2 + (70 - 101)2 + (100 - 101)2 + (90 - 101)2 + (110 - 101)2 + (120 - 101)2 + (95 - 101)2 = 3390 SSY = ∑ (Y – MY )2 = (80 - 75.3)2 + (72- 75.3)2 + (75 - 75.3)2 + (93 - 75.3)2 + (61 - 75.3)2 + (66 - 75.3)2 + (71 - 75.3)2 + (80 - 75.3)2 + (90 - 75.3)2 + (65- 75.3)2 = 1000.1 Step 4: Measure the covariability of X and Y together SP = ∑ (X - MX ) (Y – MY ) = (105 - 101)(80 - 75.3) + (85 - 101)(72- 75.3) + (95 - 101)(75 - 75.3) + (140 - 101)(93 - 75.3) + (70 - 101)(61 - 75.3) + (100 - 101)(66 - 75.3) + (90 - 101)(71 - 75.3) + (110 - 101)(80 - 75.3) + (120 - 101)(90 - 75.3) + (95 - 101)(65 - 75.3) = 1647 Step 5 : Solve Pearson Correlation (r): ? = ?? √?????? = 1647 √(3390)(1000.1) = 0.8944 = 0.89 (2.d.p) For the subsequent steps, I will be testing the significance for the correlation by using a non-directional test Step 6: State the hypotheses The null hypothesis H0: Population correlation ρ = 0 The Alternative Hypothesis H1: Population correlation ρ ≠ 0 Step 7: From the t statistics, ???? = ????−? ?? = ????−? √1−???? 2 ?−2 = 0.8944 −0 √1−(0.8944 ) 2 10−2 = 0.8944 0.1581 = 5.6571= 5.657 (3.d.p) From the t table, df = 10-2 =8 and α = 0.05 (2-tailed) , I found that tcrit = 2.306. Since |tobt| > 2.306, I decide to reject H0 and conclude that there is a significant positive correlation between IQ score and Math Score in the population. b. She then wants to predict math performance from IQ. Can you find the prediction equation for her? (3 points) Yes, I can find the prediction equation by using Linear Regression . Equation for the regression line: Since SP = 1647 and SSX = 3390, I can deduce that : ? = ?? ??? = 1647 3390 = 0.4858 = 0.486 (3. ?. ?) ?=?Y – ??X = 75.3 - 0.486 × 101 = 26. 214 = 26.21 (2.?.?) Therefore, the equation is: �̂� = ?. ??? ? + ??. ?? c. One new student joined the class, but his math score was not on record. However, Amy found that his IQ score was 20 points higher than the student average in class. What would be the student’s math score? (2 points) The new IQ score of the new student = 101 + 20 = 121
Answered Same DayNov 07, 2021

Answer To: 8375a487-749e-44cc-a38c-2397df4e7323.pdf Submission via Turnitin Be as concise as possible. Total:...

Medhini answered on Nov 07 2021
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8375a487-749e-44cc-a38c-2397df4e7323.pdf
Submission via Turnitin
Be as concise as possible. Total: 25 points
Part A. Multiple Choice Questions (5 points, 1 point each question)
A1.    When we conduct t-test, we have to be cau
tious about the structure of our data.
Which in 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...
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