Question

Measurements were taken from snails of the shell weights and the widths of the opercula. Plot a graph of opercula width (y-axis) versus shell weight (x-axis). Estimate the correlation coefficient and test to see if there is a significant association shell weights and the widths of the opercula. Use a 5% level of significance.

Opercula width
Shell weight (g) (mm)
12 10.1
10 9.0
7 5.5
14 9.9
11 8.3
8 8.5
10 8.0
9 6.4
6 6.2
13 8.1 2.306

Answer 1

Yes,there is a significant association shell weight and the widths of the opercula

Explanation:

Using a correlation Coefficient calculator :

Given the data above :

The Coefficient of correlation(r) obtained is :

0.7632

Obtaining the test statistic :

T = r² / √(1 - r²) / (n - 2)

T = 0.7632² / √(1 - 0.7632²) / (10 - 2)

T = 0.58247424 / 0.2284528

Test statistic = 2.550

The Pvalue from r score , N = 10

Pvalue(0.7632, 10) = 0.01022

α = 0.05

If Pvalue < α ; reject H0

Pvalue < α ; We conclude that there is a significant association shell weights and the widths of the opercula