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Growing tomatoes An agricultural field trial compares the yield of two varieties of tomatoes for commercial use. Researchers randomly selected 10Variety A and 10 Variety B tomato plants. Then the researchers divide in half each 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 10differences (VarietyA-VarietyB) give x=0.34andsx=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 =0.05to answer the question.

Short Answer

Expert verified

Since the P-value is greater than 0.05, we fail to reject H0. We do not have enough evidence to conclude that Variety A has a higher mean yield than Variety B.

Step by step solution

01

Given information

Researchers randomly selected 10Variety A and 10Variety B tomato plants.

Then the researchers divide in half each 10small 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 (VarietyA-VarietyB) give x=0.34and sx=0.83.

02

Explanation

State: H0:=0,Ha:>0Plan: Random: Random assignment.

Normal: Graph of the data is roughly symmetric with no outliers.

Independent: There are more than 100plants of each variety.

Do:t=1.295,P-value=0.1138.

Conclude: Since the P-value is greater than 0.05, we fail to reject H0. We do not have enough evidence to conclude that Variety A has a higher mean yield than Variety B.

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