Report the following: State the null (H0) and alternative (H1) hypotheses. Assum
ID: 3156898 • Letter: R
Question
Report the following:
State the null (H0) and alternative (H1) hypotheses.
Assume = 0.05, two-tails; report values for df and rcrit [1 pt] Fill in the missing values in the data table above to show your INITIAL computations
Report values for SPXY SSX SSY and Pearson’s r
State your decision regarding the null hypothesis, H0.
Indicate whether the relationship between X and Y is “negative” or “positive”
Indicate whether the relationship between X and Y is “weak” or “medium” or “strong” according to Cohen’s guidelines for the value of Pearson’s r.
Report the value of the proportion of variability in Y accounted for by X.
Write 1 sentence interpreting the value you computed.
Write 1 sentence demonstrating how the results of this specific hypothesis test would appear in a research report
X Y X2 Y2 XY 2 0 3 1 7 4 5 6 4 6 3 6 X= Y= X2= Y2= XY=Explanation / Answer
Here we have given data of x and y values.
Report the following:
State the null (H0) and alternative (H1) hypotheses.
Assume = 0.05, two-tails; report values for df and rcrit [1 pt] Fill in the missing values in the data table above to show your INITIAL computations.
Here we have to test he hypothesis that,
H0 : There is no correlation between x and y.
H1 : There is correlation between x and y.
Assume alpha = level of significance = 5% = 0.05
Report values for SPXY SSX SSY and Pearson’s r
The correlation coefficient formula is,
r = n*(xy) - (x)(y) / sqrt [n*x2 - (x)2 ] * [n*y2 - (y)2 ]
= (6*103 - 24*23) / sqrt [6*112 - 242]*[6*125 - 232]
= 66/sqrt(96*221)
= 66/145.66
r = 0.4531
The test statistic is,
t = r*sqrt(n-2) / sqrt(1-r2)
= 0.4531*sqrt(6-2) / sqrt(1-0.45312)
= 0.9062/0.8915
t = 1.017
Now we have to find P-value :
P-value in EXCEL is,
=TDIST(x, deg_freedom,tails)
where x is tests statistic value.
deg_freedom = n-2 = 6-2 = 4
tails = 2
P-value = 0.3668
P-value > alpha
Accept H0 at 5% level of significance.
Conclusion : There is no correlation between x and y.
Report the value of the proportion of variability in Y accounted for by X.
proportion of variability in Y accounted for by X = r2 = 0.45312 = 0.2053
x y x^2 y^2 xy 2 0 4 0 0 3 1 9 1 3 7 4 49 16 28 5 6 25 36 30 4 6 16 36 24 3 6 9 36 18 24 23 112 125 103