Question

The data below shows height (in inches) and pulse rates (in beats per minute) of a random sample of women. Find the value of the linear correlation coefficient r, using a significance level of 0.05 Is there sufficient evidence to conclude that there is a linear correlation between height and pulse rate?

Height | Pulse Rate

61.7    80

64.3    74

60.1    89

60.3 61

59.3 75

61.5 66

59.6    83

61.1    61

67.5    68

59.7 68

67.1 81

63.3 76

61.8 70

58.9    74

59.2 71

59.5    72

66.6    83

60.8 79

69.6 76

58.2 76

Answer 1

Let x bet the height and y be the  pulse rate.

The given data is

linear correlation coefficient r is given as

Now obtaining the

From the calculations

Therefore

= 0.129691

Testing the significance of correlation coefficient

be the correlation coefficient for population

The null hypothesis is given as

i.e there is no linear correlation

i.e there is a linear correlation .

The test statistic is given as

r= 0.129691

n= 20

= 0.554919

The degree of freedom is given as

df = n-2

= 18

Obtaining the p-value

Since the p-value is > 0.05 =

We failed to reject the null hypothesis.

There is no a significant correlation between height and pulse rate.