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)?

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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)?
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
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 (α) = 0.05

 

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