Hypothesis test of Pearson’s product-moment correlation coefficient
9
The following are values of the product moment correlation coefficient between the \(x\) and \(y\) values of three different large samples of bivariate data. State what each indicates about the appearance of a scatter diagram illustrating the data.
- 1 ,
0.02 ,
0.92 .
In 1852 Dr William Farr published data on deaths due to cholera during an outbreak of the disease in London. The table shows the altitude (in feet, above the level of the river Thames) at which people lived and the corresponding number of deaths from cholera per 10000 people.
Altitude, \(x\)
10
30
50
70
90
100
350
Number of deaths, \(y\)
102
65
34
27
22
17
8
$$\left[ \Sigma x = 700 , \Sigma x ^ { 2 } = 149000 , \Sigma y = 275 , \Sigma y ^ { 2 } = 17351 , \Sigma x y = 13040 . \right]$$
Calculate the product moment correlation coefficient.
Test, at the \(5 \%\) significance level, whether there is evidence of negative correlation.