SCENARIO 11-11
an Agronomist Wants to Compare the Crop Yield

question 47

Short Answer

SCENARIO 11-11
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3
varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in
bushels per acre. Treating this as a randomized block design, the results are presented in the table that
follows. $\begin{array}{rrrr}\underline {\text { Fields }} &\underline {\text { Smith}}& \underline{\text {Walsh}}& \underline{\text {Trevor }}\\1&11.1 & 19.0 & 14.6 \\2&13.5 & 18.0 & 15.7 \\3&15.3 & 19.8 & 16.8 \\4&14.6 & 19.6 & 16.7 \\5&9.8 & 16.6 & 15.2\end{array}$
-Referring to Scenario 11-11, the null hypothesis for the randomized block F test for the difference in the means is a) $H _ { 0 } : \mu _ { \text {.Field } 1 } = \mu _ { \text {.Field } 2 } = \mu _ { \text {.Field } 3 } = \mu _ { \text {.Field } 4 } = \mu _ { \text {.Field } 5 }$
b) $H _ { 0 } : \mu _ { \text {.Smith } } = \mu _ { \text {.Walsh } } = \mu _ { \text {.Trevor } }$
c) $H _ { 0 } : M _ { \text {.Field 1 } } = M _ { \text {.Field } 2 } = M _ { \text {.Field } 3 } = M _ { \text {.Field } 4 } = M _ { \text {.Field } 5 }$
d) $\quad H _ { 0 } : M _ { \text {.Smith } } = M _ { \text {.Walsh } } = M _ { \text {.Trevor } }$

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Definitions:

Consistent Estimator

An attribute of an estimator indicating that as the sample size increases, the estimates it produces converge in probability to the parameter being estimated.

Sample Mean

The mean value derived from a dataset sample, utilized to predict the overall population's average.

Sampling Distribution

The probability distribution of a statistic (like a mean) derived from a large number of samples of a population.

Unbiased Estimators

Statistical estimators that are expected to equal the population parameter over many samples.