Question

A farmer is interested in comparing three different brands of
fertilizer, Grow'em Big, Jim's Fertilizer and Sally's Best. He
planted wheat in 4 different fields, one with each brand of
fertilizer and the fourth one with no fertilizer as a control. Each
field is 69 acres in size. The farmer recorded the yield in bushels
for each acre of every field. They are interested in knowing
whether certain brands of fertilizer have an impact on yield.
Assume that the mean of the control is μ_{1}, Grow'em Big
is μ_{2}, Sally's Best is μ_{3} and Jim's
Fertilizer is μ_{4}. The summary statistics for the
farmer's experiment are as follows:

Control | Grow'em Big | Jim's Fertilizer | Sally's Best | |

Mean | 22.01 | 25.35 | 45.41 | 23.50 |

Sum of Squares: | 33951.24 | 78820.37 | 221676.00 | 260258.25 |

**How many pairwise comparisons is the farmer
making?**

**Assuming a confidence level of 95 %, what would be the
value of α ^{*}**

^{(I tried 0.05 its incorrect)}

**For μ _{1}−μ_{4} (control vs. Jim's
Fertlizer) do we reject the null hypothesis? F**

Answer #1

**pairwise comparisons = 3**

**================**

**α* = 0.05/3 = 0.0167**

==============

no. of treatments,k= 4

DF error =N-k= 272

MSE= 2186.4186

**t-critical value,t(α/2,df)=
2.4089**

confidence interval |
||||||

mean difference | critical value | lower limit |
upper limit |
|||

µ1-µ2 |
-3.34 | 19.18 | -22.5166 |
15.8366 |
||

µ1-µ3 |
-1.49 | 19.18 | -20.6666 |
17.6866 |
||

µ1-µ4 |
-23.40 | 19.18 | -42.5766 |
-4.2234 |

if confidence interval do not contains zero, then means are
significantly different.

**For μ _{1}−μ_{4} (control vs. Jim's
Fertlizer) do we reject the null hypothesis?**

**answer: YES**

**=============**

**F****or μ _{1}−μ_{3}
(control vs. Sally's Best), do we reject the null
hypothesis?**

**answer: NO**

**-------------**

**And for μ _{1}−μ_{2} (control vs. Grow'em
Big), do we reject the null hypothesis?**

**answer: NO**

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