Question

13. 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 a=0.05. Is there sufficient evidence to conclude that there is a linear correlation between height and pulse​ rate?

height_(x)           pulse_rate_(y)

61.2        75

67.8        73

60.1        88

60.1        64

59.3        71

60.9        70

59.5        83

60.8        65

67.8        67

59.9        70

67.9        84

62.8        79

60.4        71

63.4        66

58.1        70

60.4        65

66.4        77

60.2        74

67.1        81

61.5        78

What are the null and alternative​ hypotheses?

Construct the scatterplot.

The linear correlation coefficient r is _____

(Round to three decimal places as​ needed.)

The test statistic t is _____

(Round to three decimal places as​ needed.)

The​ P-value is ______

(Round to three decimal places as​ needed.)

Because the​ P-value is (greater,less) than the significance level 0.05​, there (is not, is) sufficient evidence to support the claim that there is a linear correlation between selling price​ (in hundred​ thousands) and the list price​ (in hundred​ thousands) of homes sold for a significance level of a=0.05.

Answer 1

	Height X	Pulse Rate Y	X * Y
	61.2	75	4590	3745.44	5625
	67.8	73	4949.4	4596.84	5329
	60.1	88	5288.8	3612.01	7744
	60.1	64	3846.4	3612.01	4096
	59.3	71	4210.3	3516.49	5041
	60.9	70	4263	3708.81	4900
	59.5	83	4938.5	3540.25	6889
	60.8	65	3952	3696.64	4225
	67.8	67	4542.6	4596.84	4489
	59.9	70	4193	3588.01	4900
	67.9	84	5703.6	4610.41	7056
	62.8	79	4961.2	3943.84	6241
	60.4	71	4288.4	3648.16	5041
	63.4	66	4184.4	4019.56	4356
	58.1	70	4067	3375.61	4900
	60.4	65	3926	3648.16	4225
	66.4	77	5112.8	4408.96	5929
	60.2	74	4454.8	3624.04	5476
	67.1	81	5435.1	4502.41	6561
	61.5	78	4797	3782.25	6084
Total	1245.6	1471	91704.3	77776.74	109107

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 0.916

Test Criteria :-
Reject null hypothesis if

-2.1009 < 0.916 < 2.1009
Result :- We fail to Reject null hypothesis

Decision based on P value
P - value = P ( t > 0.916 ) = 0.372
Reject null hypothesis if P value <    level of significance
P - value = 0.372 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- We Accept H0

Because the​ P-value is (greater ) than the significance level 0.05​, there (is not ) sufficient evidence to support the claim that there is a linear correlation between height and pulse rate at significance level of a=0.05.