The Following Data Shows the Yield, in Bushels Per Acre

question 25

Essay

The following data shows the yield, in bushels per acre, categorized according to three varieties of corn and
three different soil conditions. Assume that yields are not affected by an interaction between variety and soil
conditions, and test the null hypothesis that variety has no effect on yield. Use a 0.05 significance level. $$\begin{array} { c c c c } & \text { Plot 1 } & \text { Plot 2 } & \text { Plot 3 } \\\text { Variety 1 } & 156,167 , & 162,160 , & 145,151 , \\& 170,162 & 169,168 & 148,155 \\\text { Variety 2 } & 172,176 , & 179,186 , & 161,162 , \\& 166,179 & 160,176 & 165,170 \\\text { Variety 3 } & 175,157 , & 178,170 , & 169,165 , \\& 179,178 & 172,174 & 170,169\end{array}$$

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Definitions:

Nonparametric Test

A type of statistical test that does not assume a specific distribution for the data, often used when data doesn't meet the assumptions required for parametric tests.

Normally Distributed

Describes a probability distribution that is symmetrical around its mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Abnormally Distributed

Indicative of a probability distribution that does not follow a normal distribution pattern, potentially skewed or featuring heavy tails.

Un-standardized Test Statistic

A test statistic that has not been converted to a standard form, representing raw effect sizes or differences observed in data.