1) (Five parts; 25 marks in total) An agronomist studied the effects of moisture
ID: 3317623 • Letter: 1
Question
1) (Five parts; 25 marks in total) An agronomist studied the effects of moisture (in inches) and temperature (in °C) on the yield of a new hybrid tomato. She chose five levels for moisture (6, 8, 10, 12, and 14) and five levels for temperature (20, 21, 22, 23, and 24), conducting an experiment with two replications for each combination of moisture and temperature. Based on the following partial computer output from two-factor ANOVA, answer parts (a) - (c) below Descriptive Statistics Variable Yield Moisture Temperature Sample MeanSample S.D 47.097 10.000 22.000 7.07121 2.85714 1.42857 Tests of Between-Subjects Effects Dependent Variable: Yield Type Ill Sum df Mean Square of Squares Source Sig Corrected Model Moisture Temperature Moisture Temp Error Corrected Total 360.465 35.219 39.467 19.240 454.391 .004Explanation / Answer
level of moisture and temp are 5 and so thier df will be 5-1=4 each
df of moisture*temp=4*4=16
total df=5*5*2-1=49
error df=total df - (moisture df + temp df+moisture*temp df)=49-(4+4+16)=25
MS=SS/df and F=MS/MS(error)
following informaiton has been generated using ms-excel
(a) There are three sets of hypothesis with the two-way ANOVA.
alternate hypothesis are
The alternative hypothesis for cases 1 and 2 is: the means are not equal.
The alternative hypothesis for case 3 is: there is an interaction between two factors.
since p-value is less than the level of significance alpha=0.01, so we fail to accept null hypothesis
(b)
null hypothesis H0:The population means of the temperatue is equal.
The alternative hypothesis Ha: means of temp are not equal.
since p-value is less than the level of significance alpha=0.01, so we fail to accept null hypothesis
Type III source SS df MeanSquare(MS) F sig corrected model 435.151 24 18.13129167 23.559 0.000 moisture 360.465 4 90.116 117.095 0.000 temperature 35.219 4 8.805 11.441 0.000 Moisture*Temp 39.467 16 2.467 3.205 0.004 Error 19.24 25 0.770 Totoal 454.391 49Related Questions
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