Question

The data below shows height​ (in inches) and pulse rates​ (in beats per​ minute) of a random sample of women. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using alphaequals0.05. Is there sufficient evidence to conclude that there is a linear correlation between height and pulse​ rate?

							Full data set
height​ (x)	64.7	66.9	61.2	60.5	59.6	63.8	59.7	63.2	67.6	60.3
pulse rate​ (y)	79	71	86	60	70	66	83	63	66	70
height​ (x)	67.8	65.9	60.7	61.4	63.3	58.2	69.3	59.8	65.1	60.4
pulse rate​ (y)	84	78	71	71	68	73	78	79	75	82

What are the null and alternative​ hypotheses?

A.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρgreater than>0

B.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρless than<0

C.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρnot equals≠0

D.

Upper H 0H0​:

rhoρnot equals≠0

Upper H 1H1​:

rhoρequals=0

Construct a scatterplot. Choose the correct graph below.

A.

64807290xy

A scatterplot has a horizontal x-scale from less than 64 to 80 in intervals of 2 and a vertical y-scale from less than 72 to 90 in intervals of 2. Twenty points are plotted with coordinates as follows: (60.5, 71); (61.5, 71); (63.5, 68); (58, 73); (60, 79); (60.5, 82); (59.5, 70); (59.5, 83); (63, 63); (60.5, 70); (61, 86); (60.5, 60); (64, 66); (64.5, 79); (66, 78); (67, 71); (68, 84); (67.5, 66); (69.5, 78); (65, 75). All horizontal coordinates are approximate.

B.

64807290xy

A scatterplot has a horizontal x-scale from less than 64 to 80 in intervals of 2 and a vertical y-scale from less than 72 to 90 in intervals of 2. Twenty points are plotted with coordinates as follows: (54, 65); (55, 68); (57, 66); (58, 69); (58, 71); (59, 70); (61, 72); (63, 76); (64, 74); (66, 78); (67, 77); (68, 75); (70, 79); (71, 80); (71, 82); (73, 80); (73, 84); (74, 83); (76, 88); (76, 85).

C.

64807290xy

A scatterplot has a horizontal x-scale from less than 64 to 80 in intervals of 2 and a vertical y-scale from less than 72 to 90 in intervals of 2. Twenty points are plotted with coordinates as follows: (52, 76); (52, 84); (52, 87); (53, 62); (53, 82); (53, 87); (56, 63); (56, 85); (58, 77); (63, 62); (64, 72); (65, 62); (65, 88); (69, 64); (69, 82); (70, 78); (74, 68); (76, 76); (77, 63); (77, 78).

D.

64807290xy

A scatterplot has a horizontal x-scale from less than 64 to 80 in intervals of 2 and a vertical y-scale from less than 72 to 90 in intervals of 2. Twenty points are plotted with coordinates as follows: (52, 86); (53, 84); (54, 79); (55, 82); (56, 82); (57, 82); (58, 78); (60, 80); (61, 77); (62, 76); (64, 78); (65, 72); (66, 75); (68, 70); (69, 73); (71, 68); (72, 70); (74, 67); (77, 62); (77, 65).

The linear correlation coefficient r is

nothing.

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

The test statistic t is

nothing.

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

The​ P-value is

nothing.

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

Is there sufficient evidence to conclude that there is a linear correlation between the two​ variables?

A.

YesYes​,

because the​ P-value is

lessless

than the significance level.

B.

YesYes​,

because the​ P-value is

greatergreater

than the significance level.

C.

NoNo​,

because the​ P-value is

greatergreater

than the significance level.

D.

NoNo​,

because the​ P-value is

lessless

than the significance level.

Answer 1

The Given Data is:

Height(x)	Pulse Rate(y)
64.7	79
66.9	71
61.2	86
60.5	60
59.6	70
63.8	66
59.7	83
63.2	63
67.6	66
60.3	70
67.8	84
65.9	78
60.7	71
61.4	71
63.3	68
58.2	73
69.3	78
59.8	79
65.1	75
60.4	82

(a) What are the null and alternative​ hypotheses?

Answer is option B.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρless than<0

(b) Construct a scatterplot. Choose the correct graph below.

Here, I plot the scatterplot by using excel scatterplot and output is as below:

The linear correlation coefficient r is

0.053

The test statistic t is

0.226

The​ P-value is

0.824

Is there sufficient evidence to conclude that there is a linear correlation between the two​ variables?

Answer is C option.

NoNo​,

because the​ P-value is

greatergreater

than the significance level.

Explanation: I have got these results by using Excel>Megastat>Regression.

Here is the output:

Regression Analysis
	r²	0.003	n	20.000
	r	0.053	k	1.000
	Std. Error	7.482	Dep. Var.	Pulse Rate(y)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	2.863	1.000	2.863	0.051	0.824
Residual	1007.687	18.000	55.983
Total	1010.550	19.000
Regression output					confidence interval
variables	coefficients	std. error	t (df=18)	p-value	95% lower	95% upper
Intercept	66.166	33.137	1.997	0.061	-3.452	135.783
Height(x)	0.119	0.526	0.226	0.824	-0.985	1.223