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For each problem provide the following: . Hypotheses . Pre-test results and tran

ID: 3360775 • Letter: F

Question

For each problem provide the following: . Hypotheses . Pre-test results and transformations (if necessary Appropriate ANOVA table . Post-test (if applicable) .Conclusion: statistical & biological 1. A botanist is studying the effects of different fertilizers on wheat growth. The wheat berry production for each type of fertilizer is found below. Does there appear to be a difference in the number of wheat berries produced depending on fertilizer type? 3. Cow 4. Chicken 1. SuperGro2. CrazyPlant 30 32 38 26 25 28 38 38 32 30 37 32 27 31 27 26 29 27 25 25 32 31 29 27 32 30 30

Explanation / Answer

Hypothesis of the data,

we are given above the table of ANOVA,

The hypotheses of interest in an ANOVA are as follows:

where k = the number of independent comparison groups.

the formulas for calculation for ANOVA,

df

ss

mss

f

p

Between

k-1

SSb

MSB=SSB/k-1

F=MSB/MSE

within

n-k

SSE

MSE=SSE/n-k

total

n-1

SST

the analysis table for anova is

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

160.1071

3

53.36905

4.261407

0.015099

3.008787

Within Groups

300.5714

24

12.52381

Total

460.6786

27

conclusion:

p-value is =0.01 , p<0.5 therefor we reject the null hypothe sis and we can conclud that the there is significant diffreance between the all groups.

Post test(Tukeys test)

The p-value corrresponing to the F-statistic of one-way ANOVA is lower than 0.05 which strongly suggests that
one or more pairs of treatments are significantly different. You have k=4k=4 treatments, for which we shall apply
Tukey's HSD test to each of the 6 pairs to pinpoint which of them exhibits statistially significant difference.

We first establish the critical value of the Tukey-Kramer HSD QQ statistic based on the k=4 treatments
and =24 degrees of freedom for the error term, for significance level =0.05 (p-values) in
the Studentized Range distribution. We obtain these ctitical values forQ for of 0.05,
critical value of Q at Q =0.05,k=4,=24 Q= 3.9015.

so in the table group B and Group C has significant diffreance from each other.

thanks.

df

ss

mss

f

p

Between

k-1

SSb

MSB=SSB/k-1

F=MSB/MSE

within

n-k

SSE

MSE=SSE/n-k

total

n-1

SST