# Define the parameter of interest

Up until this point in the course, you have used descriiptive statistics, examined the data numerically and graphically. The next step is answering the research questions using inferential statistics.

Descriiptive statistics describe the data in the sample. Inferential statistics uses the results of the descriiptive analysis and allows students to make inferences about the population from which the sample was drawn. Hypothesis testing is used to make these inferences.

Using SAS, provide the steps needed to evaluate a continuous dependent and continuous independent variable. You must show all 5 steps and consider assumptions.

The 5 steps are:

Define the parameter of interest.

State the hypothesis.

Determine the test statistic and p-value considering necessary assumptions.

Reject or Not Reject the null hypothesis

State the conclusion in context of the problem

Material to help with assignment:::

The Week 5 and 6 resources do not give you what you need to do the assignments well. The Week 5 lecture slides provided don’t align with the assignment for the week nor do they really show you the steps needed in hypothesis testing for two continuous variables (they discuss proportions, which is part of the Week 6 assignment). And the assignment does not make it clear that you are using your final project questions on this week’s (and next week’s assignment).

In order for you to do these assignments well I am providing you with the old explanatory lectures for Week 5 and 6 from last term, which are excellent. They are below…please watch them. Also, I am including the slides for them so you can use them as guidance when doing your assignment, which is also part of the final project. After the lecture and slide links you will see new assignment instructions for Week 5, which include an example, as we had last term. Please note that this example ONLY applies to the two continuous variables question in Week 5. You will not use correlation in Week 6 when you answer the other two research questions. In Week 6 you have to choose the correct test based on those lectures, so review them carefully. If you watch these videos and read the new instructions you should be OK for both weeks’ assignments.

Best, Dr. Hunt (see below)

Old lectures and slides by Dr. O’Brien for hypothesis testing

https://drive.google.com/file/d/1q9USpmChdpmue3PqlNBVZWHe7cuFPmQP/view

https://drive.google.com/file/d/1AGqYs1WYu9v1qna04GOeonDWtXxusmuG/view

Clarified Week 5 Assignment Instructions:

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

Test statistic: Report the correlation test statistic from SAS. The p-value is 0.048 and I have 48 degrees of freedom. I should check my 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 my alpha level of .05, I reject the null hypothesis of no correlation.

Conclusion: I 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.

Your submission needs to clearly discuss each step to properly evaluate your primary research question. You should divide up your document with subheadings for each step. Be sure to restate your research questions at the beginning of your assignment.

https://drive.google.com/drive/folders/1evvtzRKlPwQvX9QOvtV3t7sqg4XCfyvD?usp=sharing