SOLVE THIS PROBLEM BY USING SPSS PROGRAM Two varieties of wheat were tested usin
ID: 3049291 • Letter: S
Question
SOLVE THIS PROBLEM BY USING SPSS PROGRAM
Two varieties of wheat were tested using two similar plots on eight different farms. One plot on each farm was selected at random to receive variety A, and the other variety B. All plots were planted on the same day and managed identically. The yields (kg/plot) 1 2345 6 7 8 Farm Variety A 17.8 18.5 12.2 19.7 10.8 11.9 15.6 12.5 Variety B 14.7 15.2 12.9 18.3 10.1 12.2 13.5 9.9 Is there evidence at the 5% significance level that the yield of the 2 varieties differ? a) b) Estimate the difference in yield with 95% confidence.Explanation / Answer
Part (a)
Let X = yield from variety A
Y = yield from variety B
Then, X ~ N(µ1, 12) and Y ~ N(µ2, 22), where 12 = 22 = 2, say and 2 is unknown.
Claim:
The yield of two varieties differ.
Hypotheses:
Null: H0: µ1 = µ2 Vs Alternative: HA: µ1 µ2
Test Statistic:
t = (Xbar - Ybar)/{s(2/n)} where
s2 = (s12 + s22)/2;
Xbar and Ybar are sample averages and s1, s2 are sample standard deviations based on n observations each on X and Y.
Calculations
Summary of Excel calculations is given below:
n =
8
Xbar =
14.875
Ybar =
13.35
s1 =
3.459046
s2 =
2.771281
s^2 =
9.8225
s =
3.134087
tcal =
0.97317
=
0.05
tcrit =
2.144787
p-value =
0.346984
Distribution, Critical Value and p-value:
Under H0, t ~ t2n - 2. Hence, for level of significance %, Critical Value = upper (/2)% point of t2n - 2 and p-value = P(t2n - 2 > | tcal |).
Using Excel Functions, the above are found to be as follows:
tcrit =
2.144787
p-value =
0.346984
Decision Criterion (Rejection Region):
Reject H0 if | tcal | > tcrit or p-value <
Decision:
Since | tcal | < tcrit, H0 is accepted. Since p-value > , H0 is accepted.
Conclusion:
There is not sufficient evidence to suggest that the claim is valid.
=> the two varieties do not differ with respect to yield.
DONE
Part (b)
100(1 - ) % Confidence Interval for (1 - 2) is: (Xbar – Ybar) ± {(t2n – 2, /2)(s)(2/n)}
= 1.525 ± (2.1448 x 3.1341 x 0.5)
= 1.525 ± 3.361
= (1.836, 4.886) ANSWER
n =
8
Xbar =
14.875
Ybar =
13.35
s1 =
3.459046
s2 =
2.771281
s^2 =
9.8225
s =
3.134087
tcal =
0.97317
=
0.05
tcrit =
2.144787
p-value =
0.346984
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