Estimate the simple linear regression equation relating female sex to GPA

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8.12 Practice Problems

1. Suppose we want to design a new placebo-controlled trial to evaluate an experimental medication to increase lung capacity. The primary outcome is peak expiratory flow rate, a continuous variable measured in liters per minute. The primary outcome will be measured after 6 months on treatment. The expected peak expiratory flow rate in adults is 300 with a standard deviation of 50. How many subjects should be enrolled to ensure 80% power to detect a difference of 15 liters per minute with a two sided test and ? = 0.05?
2. An investigator wants to estimate caffeine consumption in high school students. How many students would be required to ensure that a 95% confidence interval estimate for the mean caffeine intake (measured in mg) is within 15 units of the true mean? Assume that the standard deviation in caffeine intake is 68 mg.
3. Consider the study proposed in problem #2. How many students would be required to estimate the proportion of students who consume coffee? Suppose we want the estimate to be within 5% of the true proportion with 95% confidence.

9.3 Practice Problems      
       
# Hours # AVG NBR #Cups     
Female Year in Current Exercise of Drinks Coffee ID Age Sex School GPA Smoker per week per week per Week
1 18 1 Fr 3.85 1 7 3 3      
2 21 0 Jr 3.27 1 3 2 4      
3 19 1 So 2.90 0 0 4 7      
4 22 0 Sr 3.65 1 0 2 4      
5 21 1 Sr 3.41 1 0 1 3      
6 20 0 Jr 3.20 0 2 5 8      
7 19 1 Jr 2.89 1 1 4 10      
8 17 0 Fr 3.75 0 6 0 0      
9 18 0 So 4.00 0 6 2 6      
10 17 1 So 3.18 0 3 5 7      
11 21 0 Jr 2.58 1 3 12 12      
12 22 1 Sr 2.98 0 2 3 4      
13 19 0 Fr 3.16 1 2 0 6      
14 21 1 Jr 3.36 1 3 1 2      
15 22 1 So 3.72 0 6 3 0      
16 19 0 So 3.30 1 4 0 6      
17 16 0 Fr 3.28 0 4 0 5      
18 22 0 Sr 2.98 0 0 8 5      
19 17 1 Fr 3.90 0 7 0 2      
20 20 1 Sr 3.78 1 4 6 2      
21 21 1 So 3.26 1 2 3 4      
22 23 0 Jr 3.01 0 1 9 7      
23 23 0 Sr 3.83 1 5 4 4      
24 17 1 Fr 3.76 0 5 2 1      
25 22 1 Sr 3.05 0 1 5 5      
       
       
1. Consider the following data measured in a sample of n=25 undergraduates in an on-campus survey of health behaviors. Enter the data into an Excel worksheet for analysis.
2. Estimate the simple linear regression equation relating number of cups of coffee per week to GPA (Consider GPA the dependent or outcome variable).
3. Estimate the simple linear regression equation relating female sex to GPA (Consider GPA the dependent or outcome variable).
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