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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 $\mathrm{Î\pm }=$0.05 to answer the question.

Step by step solution

01

Given Information

The sample size is n = $10$

significance level $\mathrm{Î\pm }$= $0.05$

sample standard deviation s = $0.83$

sample mean$\stackrel{-}{x}=0.34$

02

Explanation

Calculating the null and alternative hypotheses,

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

Using,

role="math" localid="1654321749367" $t=\frac{\stackrel{-}{x}−\mathrm{μ}}{\frac{s}{\sqrt{n}}}=\frac{0.34-1}{{\displaystyle \frac{0.83}{\sqrt{10}}}}=0.114$

The p-value is = $0.114>\mathrm{Î\pm }=0.05$

The null hypothesis isn't rejected.

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

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