State appropriate hypotheses for the paired t test. Be sure to define your parameter. What are the degrees of freedom for the paired t test? Interpret the P-value in context. What conclusion should the researchers draw? Describe a Type I error and a Type II error in this setting. Which mistake could researchers have made based on your answer to part (c)?
State appropriate hypotheses for the paired t test. Be sure to define your parameter. What are the degrees of freedom for the paired t test? Interpret the P-value in context. What conclusion should the researchers draw? Describe a Type I error and a Type II error in this setting. Which mistake could researchers have made based on your answer to part (c)?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![87. Growing tomatoes Researchers suspect that Variety A
tomato plants have a higher average yield than Variety
B tomato plants. To find out, researchers randomly
select 10 Variety A and 10 Variety B tomato plants.
Then the researchers divide in half each of 10 small
plots of land in different locations. For each plot, a
coin toss determines which half of the plot gets a Va-
riety 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 in yield
(Variety A - Variety B) are recorded. A graph of the
differences looks roughly symmetric and single-peaked
with no outliers. A paired t test on the differences
yields t = 1.295 and P-value = 0.1138.
(a)
State appropriate hypotheses for the paired t test. Be
sure to define your parameter.
(b)
What are the degrees of freedom for the paired t test?
(c) Interpret the P-value in context. What conclusion
should the researchers draw?
(d)
Describe a Type I error and a Type II error in this
setting. Which mistake could researchers have made
based on your answer to part (c)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff62bfeea-6ac7-45b6-a695-04e5c0c5ecd2%2F057a30aa-448b-4d65-8196-7459ce3653ea%2Fzl2s73a_processed.png&w=3840&q=75)
Transcribed Image Text:87. Growing tomatoes Researchers suspect that Variety A
tomato plants have a higher average yield than Variety
B tomato plants. To find out, researchers randomly
select 10 Variety A and 10 Variety B tomato plants.
Then the researchers divide in half each of 10 small
plots of land in different locations. For each plot, a
coin toss determines which half of the plot gets a Va-
riety 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 in yield
(Variety A - Variety B) are recorded. A graph of the
differences looks roughly symmetric and single-peaked
with no outliers. A paired t test on the differences
yields t = 1.295 and P-value = 0.1138.
(a)
State appropriate hypotheses for the paired t test. Be
sure to define your parameter.
(b)
What are the degrees of freedom for the paired t test?
(c) Interpret the P-value in context. What conclusion
should the researchers draw?
(d)
Describe a Type I error and a Type II error in this
setting. Which mistake could researchers have made
based on your answer to part (c)?
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
The dependent variable is the yield.
The yield is measured for the type A tomato plants and the type B tomato plants.
The test statistic is,
No. of plants (n1 = n2) = 10
t = 1.295
P-value = 0.1138
Assume the Level of significance () = 0.05
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