The table shows the overall scores and cost per load for eight detergents. The o

Question

The table shows the overall scores and cost per load for eight detergents. The overall score represents the cleaning test results for the detergent. At alpha = .01, can you conclude that there is a correlation between the overall score and the price? (Use the Spearman rank correlation) The contingency table shows a random sample of engineering, psychology, and biology articles and if and how they were coauthored. At alpha = .10, can you conclude that subject matter and co-authorship are related?

Explanation / Answer

Null Hypothesis : H0 : There is no strong correlationship between both coefficent. B= 0

Alternative HYpotheiss : Ha : There is a strong correlationship between both coefficents. B>0

Here

Result Details

X Ranks
Mean: 4.5
Standard Dev: 2.43

Y Ranks
Mean: 4.5
Standard Dev: 2.42

Combined
Covariance = 8 / 7 = 1.14
R = 1.14 / (2.43 * 2.42) = 0.194

R = CoVariance / (XRa St. Dev. * YRa St. Dev.)

Key

XRa = Ranks of X Values; YRa = Ranks of Y Values
XRa - Mx = X rank minus mean of X ranks
YRa - My = Y rank minus mean of Y ranks
Sum Diffs = (XRa - Mx) * (YRa - My)

The value of R is 0.19394 and the two-tailed value of P is 0.64537. By normal standards, the association between the two variables would not be considered statistically significant.

Q.2

Here we will perform the Chi - square test

Null HYpothesis : H0 : there is no relation with subject matter and coauthorship.

Alteernative Hypothesis : Ha : There is a strong significant relationship in between subject matter and coauthorship.

Observed table here

Here it the expected table

Chi - square difference table

X2 = sumation of (Oi -Ei )2 /Ei

Value of chi - square

X2 = 5.61

HEre for dF = (3-1) * (3-1) = 4 and dF = 0.10

value fo critical chi - square X2critical =7.779

so here X2 <  X2critical so we can reject the null hypothesis and can conclude that co- authorship is independent of subject matter.

Price(Cents) (Y) Xra Xra-Mx Yra Yra-My sum diffs 17 8.00 3.50 4.50 0.00 0.00 17 6.50 2.00 4.50 0.00 0.00 19 6.50 2.00 6.50 2.00 4.00 19 5.00 0.50 6.50 2.00 1.00 10 4.00 -0.50 2.00 -2.50 1.25 5 3.00 -1.50 1.00 -3.50 5.25 21 2.00 -2.50 8.00 3.50 -8.75 14 1.00 -3.50 3.00 -1.50 5.25

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