evaluate the continuous response and continuous explanatory variable research question and perform the appropriate hypothesis test with SPSS. Make sure you explicitly show all five steps and consider any necessary assumptions that were discussed in the lecture. These steps are:

1. Define the parameter of interest,
2. State the hypotheses,
3. Determine the test statistic and p-value considering any necessary assumptions,
4. Decide whether to reject or not reject the null hypothesis,
5. Clearly state a conclusion in the context of the problem.

Now apply these steps and submit your results. Follow the example below as a guide.

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:

1. 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)
2. Hypothesis : H0: = 0; HA: not = 0
3. Test statistic:I may not get a test statistic with SPSS, but it can be calculated to be 2.02 for this data. 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.
4. Decision: Since the p-value is less than my alpha level of .05, I reject the null hypothesis of no correlation.
5. 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
6. My data. below

Ten variables of the data set of interest and categorical or continuous:

Age(Continuous - Ratio): The age of the participant.

Sex (Categorical - Dichotomous): The participant's gender (Male/Female).

LDL Cholesterol (Continuous - Ratio): The low-density lipoprotein cholesterol level in the blood.

HDL Cholesterol (Continuous - Ratio): The high-density lipoprotein cholesterol level in the blood.

Blood Pressure (Continuous-Interval): The participant's blood pressure reading.

Hypertension Treatment(Categorical - Dichotomous): Whether the participant is being treated for hypertension (Yes/No).

Diabetes(Categorical - Dichotomous): Whether the participant has diabetes (Yes/No).

Smoking(Categorical - Dichotomous): Whether the participant is a smoker (Yes/No).

Heart Rate (Continuous - Ratio): The participant's heart rate.

Heart Rate Variability (Continuous - Ratio): The participant's heart rate variability.

Three Proposed Research Questions Using Variables Selected:

1. Is there a correlation between age and LDL cholesterol levels? This question investigates the relationship between the age of the participant (a continuous ratio variable) and their LDL cholesterol levels (another continuous ratio variable). This correlation can help us understand how age influences LDL cholesterol levels, which is a key risk factor for cardiovascular diseases. A strong correlation could inform preventative measures or treatments for high cholesterol as people age.

1. Does the treatment of hypertension affect heart rate variability? This question explores the relationship between whether a participant is being treated for hypertension (a categorical dichotomous variable) and heart rate variability (a continuous ratio variable). This question is important because it can demonstrate the efficacy of hypertension treatments. Heart rate variability is a marker or possible indicator of heart health, and understanding its relationship with hypertension treatment could lead to improved management strategies for patients with hypertension.

1. Are smoking habits associated with higher blood pressure?This question examines the relationship between a participant's smoking status (a categorical dichotomous variable) and their blood pressure (a continuous interval variable). This question is valuable because it explores the potential effects of smoking on blood pressure, another key risk factor for cardiovascular diseases. The results could further prove the importance of smoking cessation programs and their role in preventing high blood pressure and related health complications.

These research questions may lead to results that improve understanding of cardiovascular-related disorders /risk factors and help develop strategies to prevent and treat cardiovascular diseases. They also display the complex nature of health outcomes, demonstrating how various factors can interact to impact health, which is a key concept in epidemiology and public health.

Reference

Framingham Heart Data Modified for Student Use (SAV)