Question

A doctor wanted to determine whether there is a relation between a​ male's age and his HDL​ (so-called good) cholesterol. The doctor randomly selected 17 of his patients and determined their HDL cholesterol. The data obtained by the doctor are in the accompanying data table. Complete parts​ (a) through​ (f) below.

1. Click the icon to view the data obtained by the doctor.

2. Click the icon to view the​ Student's t-distribution table.

​(a) Draw a scatter diagram of the​ data, treating age as the explanatory variable. What type of​ relation, if​ any, appears to exist between age and HDL​ cholesterol?

A. There does not appear to be a relation.

B. The relation appears to be nonlinear.

C. The relation appears to be linear.

​(b) Determine the​ least-squares regression equation from the sample data.

y = _____ X + _____

​(Round to three decimal places as​ needed.)

​(c) Are there any outliers or influential​ observations?

Yes

No

​(d) Assuming the residuals are normally​ distributed, test whether a linear relation exists between age and HDL cholesterol levels at theα=0.01 level of significance.

What are the null and alternative​ hypotheses?

A.

H0: β=0

H1: β=/=0

B.

H0: β=0

H1: β>0

C.

H0: β=0

H1: β<0

D.

H0: β=/=0

H1: β=0

Calculate the test statistic.

t0=_____

​(Round to two decimal places as​ needed.)

Determine the range of the​ P-value for this hypothesis test. Choose the correct answer below.

A.The​ P-value is less than 0.001

B.The​ P-value is between 0.3 and 0.4

C.The​ P-value is between 0.4 and 0.5

D.The​ P-value is between 0.1 and 0.2

What conclusion can be drawn at alphaαequals=0.01 level of​ significance?

A.

Reject the null hypothesis because the​ P-value is greater than or equal to α=0.01

B. Reject the null hypothesis because the​ P-value is less than α=0.01

C. Do not reject the null hypothesis because the​ P-value is less than α=0.01

D. Do not reject the null hypothesis because the​ P-value is greater than or equal to α=0.01

​(e) Assuming the residuals are normally​ distributed, construct a​ 95% confidence interval about the slope of the true​ least-squares regression line.

Lower Bound = _____

Upper Bound = _____
​(f) For a​ 42-year-old male patient who visits the​ doctor's office, would using the​ least-squares regression line obtained in part​ (b) to predict the HDL cholesterol of this patient be​ recommended?​(Round to three decimal places as​ needed.)

Should this​ least-squares regression line be used to predict the​ patient's HDL​ cholesterol?

A. ​No, because the confidence interval about the slope of the true​ least-square regression line indicates that there is a linear relationship between age and HDL cholesterol levels.

B. ​Yes, because the hypothesis test indicates that there is a linear relationship between age and HDL cholesterol levels.

C. No, because the hypothesis test indicates that there is not a linear relationship between age and HDL cholesterol levels.

D. Yes, because the confidence interval about the slope of the true​ least-square regression line indicates that there is a linear relationship between age and HDL cholesterol levels.

A good estimate for the HDL cholesterol of this patient is _____

​(Round to two decimal places as​ needed.)

1: Age vs. HDL Cholesterol data

​Age, x	HDL​ Cholesterol, y	​Age, x	HDL​ Cholesterol, y
40	57	37	46
41	52	64	61
48	33	30	54
30	56	51	34
57	35	29	45
53	39	50	39
60	42	48	54
59	38	41	26
25	47

Answer 1