Researchers in a clinical study collected information from their subjects at the beginning of the study. Two of the variables were body mass index (BMI) and age. We are interested in seeing if there is an association between these two variables. The data from the study can be found in the file AgeBMI. (a) Describe the population slope in the context of the study and assign a symbol to it.
(b) State the appropriate null and alternative hypotheses in terms of the population slope using the symbol used in part (a).
(c) Is a theory-based test appropriate? Why or why not?
(d) Use a theory-based approach to find the p-value.
(e) Summarize your conclusion based on the p-value reported in part (b).
(f) If you were testing to determine if there was a positive association between age and BMI, what is the theory-based p-value?

Data:

Age bmi
35 22.3
47 24.5
32 24
35 28.1
26 29.7
38 23
45 20.2
32 22.4
29 21.5
31 24.1
27 26.9
36 33.9
58 47.4
24 42.9
56 31.8
46 28.6
54 42.4
39 43
33 33.3
43 52.5
43 52.8
46 38
39 57.6
29 31
21 29.6
53 47.1
45 28.5
45 38.3
54 30.3
45 44.6
49 43.3
32 30.5
46 49.5
39 31.3
28 28
27 47.9
42 33.4
45 36
26 42.8