Answered: A 10-year study conducted by the…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Question

A 10-year study conducted by the American heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period.

Risk	Age	Pressure	Smoker
12	57	152	No
24	67	163	No
13	58	155	No
56	86	177	Yes
28	59	196	No
51	76	189	Yes
18	56	155	Yes
31	78	120	No
37	80	135	Yes
15	78	98	No
22	71	152	No
36	70	173	Yes
15	67	135	Yes
48	77	209	Yes
15	60	199	No
36	82	119	Yes
8	66	166	No
34	80	125	Yes
3	62	117	No
37	59	207	Yes

(a)

Develop an estimated regression equation that relates risk of a stroke to the person's age, blood pressure, and whether the person is a smoker. (Let x₁ represent age, x₂ represent blood pressure, x₃ represent whether the person is a smoker, and y represent risk. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker. Round your constant term to one decimal place and coefficients to two decimal places.)

ŷ =

(b)

Is smoking a significant factor in the risk of a stroke? Explain. Use ? = 0.05.

State the null and alternative hypotheses.

H₀: β₃ = 0
H_a: β₃ ≠ 0H₀: β₃ ≤ 0
H_a: β₃ > 0 H₀: β₃ = 0
H_a: β₃ > 0H₀: β₃ ≥ 0
H_a: β₃ < 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Do not reject H₀. There is insufficient evidence to conclude that smoking is a significant factor.Do not reject H₀. There is sufficient evidence to conclude that smoking is a significant factor. Reject H₀. There is insufficient evidence to conclude that smoking is a significant factor.Reject H₀. There is sufficient evidence to conclude that smoking is a significant factor.

(c)

What is the probability of a stroke over the next 10 years for Art Speen, a 69-year-old smoker who has blood pressure of 185? (Round your answer to four decimal places.)

What action might the physician recommend for this patient?

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Risk	Age	Pressure	Smoker
12	57	152	No
24	67	163	No
13	58	155	No
56	86	177	Yes
28	59	196	No
51	76	189	Yes
18	56	155	Yes
31	78	120	No
37	80	135	Yes
15	78	98	No
22	71	152	No
36	70	173	Yes
15	67	135	Yes
48	77	209	Yes
15	60	199	No
36	82	119	Yes
8	66	166	No
34	80	125	Yes
3	62	117	No
37	59	207	Yes

Risk	Age	Pressure	Smoker
12	57	152	No
24	67	163	No
13	58	155	No
56	86	177	Yes
28	59	196	No
51	76	189	Yes
18	56	155	Yes
31	78	120	No
37	80	135	Yes
15	78	98	No
22	71	152	No
36	70	173	Yes
15	67	135	Yes
48	77	209	Yes
15	60	199	No
36	82	119	Yes
8	66	166	No
34	80	125	Yes
3	62	117	No
37	59	207	Yes

Risk	Age	Pressure	Smoker
12	57	152	No
24	67	163	No
13	58	155	No
56	86	177	Yes
28	59	196	No
51	76	189	Yes
18	56	155	Yes
31	78	120	No
37	80	135	Yes
15	78	98	No
22	71	152	No
36	70	173	Yes
15	67	135	Yes
48	77	209	Yes
15	60	199	No
36	82	119	Yes
8	66	166	No
34	80	125	Yes
3	62	117	No
37	59	207	Yes