5

Perform a hypothesis test using Table 5 in Appendix B (t-distribution table) to make a conclusion about the correlation coefficient: Ata = 0.01,n = 7, and = 0.979,...

Question

Perform a hypothesis test using Table 5 in Appendix B (t-distribution table) to make a conclusion about the correlation coefficient: Ata = 0.01,n = 7, and = 0.979, i5 there enough evidence to conclude that there is a significant correlation between the data? correlation) Ho:correlation)Ha:0 =d,f =critical values: -0rejection regions:Round to the nearest thousandthstandardized test statistic {=There iSBecause t iS'significance " conclude that there i5 & %6 level ofat thesignificant

Perform a hypothesis test using Table 5 in Appendix B (t-distribution table) to make a conclusion about the correlation coefficient: Ata = 0.01,n = 7, and = 0.979, i5 there enough evidence to conclude that there is a significant correlation between the data? correlation) Ho: correlation) Ha: 0 = d,f = critical values: -0 rejection regions: Round to the nearest thousandth standardized test statistic {= There iS Because t iS 'significance " conclude that there i5 & %6 level of at the significant linear correlation:



Answers

Construct a scatterplot, and find the value of the linear correlation coefficient $r$ Also find the $P$ -value or the critical values of $r$ from Table $A$ -6. Use a significance level of $\alpha=0.05 .$ Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section $10-2$ exercises.)Repeat the preceding exercise using diameters and volumes.

In this exercise, we refer back to exercise 24 where we found the correlation coefficient between the maximum squat weight and the jump height for individuals, And the correlation coefficient was .756. For this exercise were asked if this is a significant finding, And we are asked to determine this at a significance level of alpha equals .05. To do this, we can use table 11 from Appendix B in the textbook And in table 11. So our sample size is 12 And so the value we get from table 11 for a size, Sample size 12 and alpha equals .05 Is .576. And we can see that our correlation coefficient R .756 is greater than the test value. And therefore we can conclude that there is a significant linear correlation between max squat weight and jump height.

This exercise extends on exercise 23 where we were given data for maximum weight and time and we were asked to find the correlation coefficient between max weight and time. Question 23. We calculated that as follows, And the correlation coefficient was -195. So now we want to test At a significant level of alpha equals .01. If the sample provides sufficient evidence of a significant linear correlation between max weight and time. Now to test this, we can use table 11 from Appendix B and the textbook. So we have alpha equals .01, we have N is equal to 12. And so if we look up and equals 12 and alpha equals .01 in table 11 We get .708. Now what we want to do is compare the absolute value of our correlation coefficient With .708 And the absolute value of our correlation coefficient is indeed greater than .708. So therefore based on the sample, we have sufficient evidence of a statistically significant linear correlation between maximum weight and time. Mhm

Looking at the data we have listed here. We would like to determine whether or not there is a significant linear correlation between C. P I and subway fare CPR being the Consumer price index. To determine this, let's input our data for subway fare and CP into our graphing calculators stat option than calculating our linear regression T test. It'll output to us that we have a correlation coefficient, which is equal to 0.973 suggesting very high positive correlation. But to determine its significance, let's take a look at our P value to determine whether or not we can trust this. R P value here is 0.979 So if our null hypothesis or that P is equal to zero and our alternative hypothesis for the P is not equal to zero, in which case, if it is equal to peer is equal to zero, we have no correlation. Whereas if it's not equal to zero, we do indeed have correlation. And because R P value is as low as it is, it would be less than any significance level we would choose would likely choose a 5% or at 1% level. So even if we were to have a 1% level of significance, we would fail to reject the null here in favor of the alternative that there is in fact significant linear correlation as represented by our our value of 0.973

Problem number five. So I didn't mind the degrees of freedom. The population variances are equal degree of freedom Equal toe in one plus in two minus two is equal to seven plus 11. Minus two is 16 and is the variances are not equal. So the minimum off in one minus 1 56 and then the two minus one, which is 10 toe, actually six. So the critical value in the row off degree of freedom with the current off off ableto open toe 51 teen Using table five, they created a very little to 94.746 and the critical value is equal to negative 1.94 for three.


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