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

height_(x)   pulse_rate_(y)
65.8   78
66.6   74
63.9   86
64.5   63
60.3   74
65.7   65
61.6   81
65.4   62
67.9   70
63.1   69
67.6   80
66.1   76
58.9   69
59.8   64
59.6   68
60.8   67
66.7   84
58.2   74
65.6   76
63.4   80

Answer the following question with the info above.

what is The linear correlation coefficient r ?

what is The test statistic t ?

what is The? P-value ?

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

A.Yes?, because the? P-value is lessthan the significance level.

B.No, because the? P-value is greater than the significance level.

C.Yes?, because the? P-value is greater than the significance level.

D.No?, because the? P-value is less than the significance level.

Answer 1

a) The Correlation Coefficient

The value of linear corrrelation coefficient r = 0.2405

b) Hypothesis Testing

Null Hypothesis

Alternative Hypothesis

Under H0, the test statistic is

Degrees of freedom = n-2=20-2=18

c) The P-Value is 0.3072

d) Answer: B.No, because the? P-value is greater than the significance level. Fail to Reject H0. hence thereis no linear correlation between X and Y.