Q. 75 - The Practice of Statistics for AP

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 $(Variety A - Variety B)$ 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.

Step-by-Step Solution

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 1: 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 $(Variety A - Variety B)$ give $x = 0.34$ and $s_x = 0.83$.

Step 2: 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.