Now that you have used descriiptive statistics and examined the data numerically and also graphically, you are ready to begin answering your research questions using inferential statistics. Descriiptive statistics describe the data in the sample, while inferential statistics allows one to take those results and hopefully make inferences about the population from which the sample was drawn. To do this, one must perform hypothesis testing.
In this assignment, you will define the steps needed to evaluate the continuous response and continuous explanatory variable research question and perform the appropriate hypothesis test with SAS. Make sure you explicitly show all five steps and consider any necessary assumptions that were discussed in the lecture.
These steps are:
Define the parameter of interest
State the hypotheses
Determine the test statistic and p-value considering any necessary assumptions
Decide whether to reject or not reject the null hypothesis
Clearly state a conclusion in the context of the problem
For example, suppose we have collected data from 50 subjects on the average number of hours slept per night and the average number of days per week of 20+ minutes of moderate exercise. We are interested in seeing if there is any relationship between hours slept and number of exercise days.
The 5-steps would be as follows:
Parameter of interest: Population correlation between the average number of hours slept per night and the number of days the subjects participated in 20+ minutes of
moderate exercise. (Note: population correlation is the appropriate parameter of interest as our two variables are continuous)
Hypothesis: H0: ρ = 0; HA: ρ not = 0 3.
Test statistic: You cannot get a test statistic with SAS for a correlation test, but it can be calculated to be 2.02 for this data. The p-value is 0.048 and you have 48 degrees of freedom. You should check the scatter plot to test if it looks roughly linear as that is an assumption, and if it does not note that here.
Decision: Since the p-value is less than an alpha level of .05, reject the null hypothesis
of no correlation.
Conclusion: Conclude that the correlation is significantly different (and larger) than 0. In the context of my research question, there is a moderately weak but statistically significant correlation between average hours slept and days per week of moderate exercise.
