Q. 75 Growing tomatoes An agricultural... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 9: Q. 75 (page 588)

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 $(V a r i e t y A - V a r i e t y B)$ 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 $伪$ $= 0.05$ to answer the question.

Short Answer

Expert verified

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 $(V a r i e t y A - V a r i e t y B)$ give $x = 0.34$ and $s_{x} = 0.83$ .

Explanation

State: $H 0 : 渭 = 0, H a : 渭 > 0$ 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: $t = 1.295, P - v a l u e = 0.1138 .$

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.