Question

Growing tomatoes 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 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 $10$differences $(VarietyA-VarietyB)$ give $x=0.34$and$s_x=0.83$. 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.

Short answer

Since the P-value is greater than $0.05$, we fail to reject $H_0$. We do not have enough evidence to conclude that Variety A has a higher mean yield than Variety B.

Step-by-step solution

Given information

Researchers randomly selected $10$Variety 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 $10$ differences $(VarietyA-VarietyB)$ give $x=0.34$and $s_x=0.83$.

Explanation

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

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

Independent: There are more than $100$plants 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 $H_0$. We do not have enough evidence to conclude that Variety A has a higher mean yield than Variety B.