The correlation coefficientris a sample statistic. What does it tell us about the value of the population correlation coefficient(Greek letter rho)? You do not know how to build the formal structure of hypothesis tests ofyet. However, there is a quick way to determine if the sample evidence based onis strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value ofrto determine if0. We do this by comparing the value |r| to an entry in the correlation table. The value ofin the table gives us the probability of concluding that0 when, in fact,= 0 and there is no population correlation. We have two choices for:= 0.05 or= 0.01.

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

x 3 6 12 17 21

y 60 95 140 172 186

r:

criticalr:

Conclusion:

Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.

Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated.

Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated.

Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.

(b) Look at the data below regarding the variablesx= lowest barometric pressure as a cyclone approaches andy= 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= 0.01. (Use 3 decimal places.)

x1004 975 992 935 984 922

y 40 100 65 145 72 153

r:

criticalr:

Conclusion:

Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.

Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.

Fail to reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.

Fail to reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.