Q.75 - The Practice of Statistics for AP

Question

An agricultural field trial compares the yield of two varieties of tomatoes for commercial use. Researchers randomly selected 10 Variety A and 10 Variety B tomato plants. Then the researchers divide half of 10 small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The 10 differences (Variety A Variety B) give $\stackrel{-}{x}$=0.34 and sx = 0.83. A graph of the differences looks roughly symmetric and single-peaked with no outliers. Is there convincing evidence that Variety A has a higher mean yield? Perform a significance test using $\alpha =$0.05 to answer the question.

Step-by-Step Solution

Answer

There is not enough convincing evidence that Variety A has a higher mean yield 

Step 1: Given Information

The sample size is n = $10$

significance level $\alpha$= $0.05$

sample standard deviation s = $0.83$

sample mean $\stackrel{-}{x}=0.34$

Step 2: Explanation

Calculating the null and alternative hypotheses,

$\begin{array}{r}{H}_0:\mu =0\\ H_a:\mu >0\end{array}$

Using,

$t=\frac{\stackrel{-}{x}-\mu }{\frac{s}{\sqrt{n}}}=\frac{0.34-1}{{\displaystyle \frac{0.83}{\sqrt{10}}}}=0.114$

The p-value is = $0.114>\alpha =0.05$

The null hypothesis isn't rejected.

Hence there is not enough convincing evidence that Variety A has a higher mean yield.