(a) Suppose n = 6 and the sample correlation coefficient is r = 0.906. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) t =   critical t =   (b) Suppose n = 10 and the sample correlation coefficient is r = 0.906. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) t =   critical t =

You wish to determine if there is a linear correlation between the two variables at a significance level of a = 0.01. You have the following bivariate data set. X y 64.4 45.7 43.9 165.3 63.9 -15.5 65.5 12.6 64 73.9 63 25.9 59.9 34.8 45.1 99.2 What is the critival value for this hypothesis test? rc.v. = What is the correlation coefficient for this data set? r = Your final conclusion is that... O There is insufficient sample evidence to support the claim the there is a correlation between the two variables. There is sufficient sample evidence to support the claim that there is a statistically significant correlation between the two variables.

The correlation coefficient r is 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 of ? yet. However, there is a quick way to determine if the sample evidence based on ? 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 ? ≠ 0. We do this by comparing the value |r| to an entry in the correlation table. The value of ? in the table gives us the probability of concluding that ? ≠ 0 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 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 ? = 0.05. (Round your answer for r to four decimal…

(a) Suppose n = 6 and the sample correlation coefficient is r = 0.892. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) t = critical t= Conclusion: O Yes, the correlation coefficient p is significantly different from 0 at the 0.01 level of significance. O No, the correlation coefficient p is not significantly different from 0 at the 0.01 level of significance. (b) Suppose n = 10 and the sample correlation coefficient is r = 0.892. Is r significant at the 1% level of significance (based on a two-tailed test)? (Round your answers to three decimal places.) t = critical t= Conclusion: O Yes, the correlation coefficient p is significantly different from 0 at the 0.01 level of significance. O No, the correlation coefficient p is not significantly different from 0 at the 0.01 level of significance. (c) Explain why the test results of parts (a) and (b) are different even though the sample correlation coefficient r =…