Question

Listed below are the overhead widths​ (in cm) of seals measured from photographs and the weights​ (in kg) of the seals. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the critical values of r using alphaequals0.01. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the​ seals?
Overhead Width 7.2 7.5 9.7 9.3 8.7 8.2Weight 119 156 243 200 199 188A. Construct a scatterplot

Answer 1

Answer and Step-by-step explanation: Scaterplot is a type of graphic which shows the relationship between to variables. In this question, you want to determine if there is a linear relationship between overhead widths of seals and the weights. So, the hypothesis are:

H₀: no linear correlation;

H₁: there is linear correlation;

In this hypothesis test, to reject H₀, the correlation coefficient r of the data set has to be bigger than the critical value from the table.

With α = 0.05 and n = 6, the critical value is 0.811.

The linear correlation is calculated as:

r = n∑xy - ∑x.∑y / √[n∑x² - (∑x)²] [n∑y² - (∑y)²]

r = $\frac{6.9632 - 51.1108}{\sqrt{6.439 - (51^{2} )}.6.14482 - (1108^{2} ) }$

r = 0.9485

Since r is bigger than the critical value, H₀ is rejected, which means there is enough evidence to conclude that there is linear correlation between overhead widths and the weights.

In the attachments is the scaterplot of the measurements, also showing the relationship.