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=0.105, n=15 a: critical values: r= +0.514, no significant linear correlations b: critical values: r= +0.514, significant linear correlation c: critical values: r= +0.532, no significant linear correlation d: critical values: r= 0.514, no significant linear correlation will mark brainliest !
r represents a significant linear correlation.
GIven : Linear correlation coefficient: r = 0.543
Sample size: n= 25
Degree of freedom : n-2 = 25-2=23
Now, we check r critical value table for value with df = 23 and .
Critical value = ±0.396 [From r critical value table]
Since r = 0.543 > 0.396, that means there is significant linear correlation.
Hence, r represents a significant linear correlation.
A: Critical values: r= ±0.514, no significant linear correlations
The correlation coefficient (r) = 0.105
Sample size (n)= 15
Significance level = 0.05
Using the Pearson Product-Moment Correlation Coefficient table:
degree of freedom (df) = n- 2
15 - 2 = 13
Looking up the table at 0.05 significance levels and a degree of freedom equals 13,
The critical value equals ±0.513977
If the correlation coefficient(0.105) obtained is greater or equal to the critical value (0.513977), then at the 0.05 significance level, a linear relationship exists between the observed variables.
However, the correlation coefficient (0.105) is less than the critical value (0.513977), therefore, no linear relationship exist.
a. Critical values : r = ±0.396, no significant linear correlation.
The critical value is 0.396 and test statistic is 0.543. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case test statistics value is greater than critical value then we should accept the null hypothesis.
C. Critical values: r = +0.396
A linear correlation for two variables X₁ and X₂ was calculated.
For a sample n= 25 the sample correlation coefficient is r= 0.767.
Be the hypotheses:
H₀: ρ = 0
H₁: ρ ≠ 0
For this hypothesis test, the rejection region is two-tailed, and the degrees of freedom are Df= n-2= 25-2= 23
So using the Pearson product-moment correlation coefficient table of critical values, under the entry for "two tailed tests" you have to cross the level of significance and the degrees of freedom to find the corresponding critical value:
Since the calculated correlation coefficient is greater than the critical value, you can reject the null hypothesis, this means that the correlation is significant at level 5%
I hope this helps!
the critical value for r at = 0.396
the linear correlation coefficient r = 0.767
the sample size n = 25
the level of significance ∝ = 0.05
The degree of freedom is expressed with the formula df = n - 2
df = 25 - 2
df = 23
the critical value for r at = 0.396
The linear correlation coefficient r = 0.767 is not in the region between the critical values of -0.396 and +0.396. We can therefore conclude that the linear correlation coefficient is significant.
t = 2.71at alpha of .05, assuming 2 tailed testcritical value is 3.182conclude it does not represent significant correlation
Also critical values for r+- .8783
With n = 9, we can find the value of df = n - 2 = 9 - 2 = 7
Then read off the table for level of significance 0.05
A screen shot is shown in the table below, hence the critical value is 0.666
The given r gives a significant linear correlation as the critical value is close to one