Question

The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient ρ (Greek letter rho)? You do not know how to build the formal structure of hypothesis tests of ρ yet. However, there is a quick way to determine if the sample evidence based on ρ is strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value of r to determine if ρ ≠ 0. We do this by comparing the value |r| to an entry in the correlation table. The value of α in the table gives us the probability of concluding that ρ ≠ 0 when, in fact, ρ = 0 and there is no population correlation. We have two choices for α: α = 0.05 or α = 0.01.

(a) Look at the data below regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of |r| large enough to conclude that weight and age of Shetland ponies are correlated? Use α = 0.05. (Use 3 decimal places.)

x	3	6	12	19	23
y	60	95	140	184	184

r
critical r

(b) Look at the data below regarding the variables x = lowest barometric pressure as a cyclone approaches and y = maximum wind speed of the cyclone. Is the value of |r| large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use α = 0.01. (Use 3 decimal places.)

x	1004	975	992	935	978	940
y	40	100	65	145	75	155

r
critical r

Answer 1

a)

you can use correl function to get correlation in excel

Using Excel

data -> data analysis -> regression

r = 0.9743

critical r for 0.05 level = 0.878

since r > critical value, there is signficant correlation

Please give me a thumbs-up if this helps you out. Thank you! :)

It is not clear what data points are, as there is no gap.

please post rest parts/ questions in a new post.