Question

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r=0.543, n = 25 

• Critical values: r = ±0.487, significant linear correlation 

• Critical values: r = ±0.487, no significant linear correlation 

• Critical values: r = ±0.396, no significant linear correlation 

• Critical values:r = ±0.396, significant linear correlation.

Answer 1

Answer :

We are given that,

Linear correlation coefficient r = 0.543,

Sample size n = 25,

Significance level = 0.05

We want to find the critical values of r.

Here critical values for r with (n - 2) = (25 - 2) = 23 degrees of freedom at alpha = 0.05 significance level for two tailed test is ±0.396.

the null hypothesis is rejected if |r| > r_c ​= 0.396.

Therefore here |r| = 0.543 > r_c= 0.396 Hence we reject the null hypothesis here.

Critical values: r = ±0.396, significant linear correlation.

Answer 2

Goebbicient 8 and Gorrelation Given the linear the sample Size ni 8 n = 25 i 8- 0.543 d: 0.05 & level pot significance So then the number Here Sample = 25, Size n ot of freedom dif-n-2 = 25 -2 =23 degrees df= = 23 The Gorresponding Critical Gorrelation Value o bor a two-tailed level d: 0.05 fox Significance test is 8c= 0.396 ie Critical values It 0.396 Significant linear Gorrelation Since 8=0.543 > 8 = 0.396 z CS Scanned with CamScanner