1. Correlations and Scatter Plots
The following data set represents avg time per week spent on social media by age for 12 randomly chosen individuals.
Age 14 18 27 21 55 46 18 26 15 17 62 41 Time (s) 240 150 135 110 45 72 150 41 200 125 31 52
a. The correlation coefficient between the two variables is found to be r = -0.84, and the standard deviation for each variable are Sage = 16.71 and Stime = 64.1. Determine the equation for the best fit line. ( To receive full points, you must show all your calculations)
b. How much time on social media does your model predict for a 21-year-old? Compare the predicted value to the observed value by calculating the residual value.
2. Sampling methods
a) A researcher is investigating the effects of online learning on K-12 education. He plans to conduct a survey that will be emailed to all parents and teachers of students by the school administrators. He decides to randomly select four schools in the district with approximately 400 students. The parents and teachers of all the students at these schools will be surveyed. Describe the sampling method being used and possible sources of sampling bias in his design.
b) A health care provider is conducting a study on the recovery process for patients who had knee surgery in their outpatient centers within the last six months. He needs a sample size of 250 and his plan is to randomly select the individuals from eight age groups 18-25, 26-30, 31-35, 36-40, 41-45, 46-50, 51-55 and 55+ from the patient database. Once selected the researcher will locate their records and follow up with a phone interview. If two age groups accounted for 50% of all the participants surveyed in the study comment on the sampling method used and the sampling biases.
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