A local "pick-your-own" farmer decided to grow blueberries. The farmer purchased and planted eight plants of each of the four different varieties of highbush blueberries. The yield (in pounds) of each plant was measured in the upcoming year to determine whether the average yields were different for at least two of the four plant varieties. The yields of these plants of the four varieties are given in the following table. Berkeley 5.13 5.36 5.20 5.15 4.96 5.14 5.54 5.22 Duke 5.31 4.89 5.09 5.57 5.36 4.71 5.13 5.30 Jersey 5.20 4.92 5.44 5.20 5.17 5.24 5.08 5.13 Sierra 5.08 5.30 5.43 4.99 4.89 5.30 5.35 5.26 a. We are to test whether the mean yields for all such bushes of the four varieties are the same. Write the null and alternative hypotheses. b. What are the degrees of freedom for the numerator and the denominator? c. Calculate SSB, SSW, and SST. d. Show the rejection and nonrejection regions on the F distribution curve for a = .01. e. Calculate the between-samples and within-samples variances. f. What is the critical value of F for a = .01? g. What is the calculated value of the test statistic F? h. Write the ANOVA table for this exercise. i. Will you reject the null hypothesis stated in part a at a significance level of 1%?
A local "pick-your-own" farmer decided to grow blueberries. The farmer purchased and planted eight plants of each of the four different varieties of highbush blueberries. The yield (in pounds) of each plant was measured in the upcoming year to determine whether the average yields were different for at least two of the four plant varieties. The yields of these plants of the four varieties are given in the following table. Berkeley 5.13 5.36 5.20 5.15 4.96 5.14 5.54 5.22 Duke 5.31 4.89 5.09 5.57 5.36 4.71 5.13 5.30 Jersey 5.20 4.92 5.44 5.20 5.17 5.24 5.08 5.13 Sierra 5.08 5.30 5.43 4.99 4.89 5.30 5.35 5.26 a. We are to test whether the mean yields for all such bushes of the four varieties are the same. Write the null and alternative hypotheses. b. What are the degrees of freedom for the numerator and the denominator? c. Calculate SSB, SSW, and SST. d. Show the rejection and nonrejection regions on the F distribution curve for a = .01. e. Calculate the between-samples and within-samples variances. f. What is the critical value of F for a = .01? g. What is the calculated value of the test statistic F? h. Write the ANOVA table for this exercise. i. Will you reject the null hypothesis stated in part a at a significance level of 1%?
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter7: Applying Fractions
Section7.1: Ratios
Problem 25WE
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Transcribed Image Text:A local "pick-your-own" farmer decided to grow blueberries. The farmer purchased and planted eight
plants of each of the four different varieties of highbush blueberries. The yield (in pounds) of each plant
was measured in the upcoming year to determine whether the average yields were different for at least two
of the four plant varieties. The yields of these plants of the four varieties are given in the following table.
Berkeley
5.13
5.36
5.20
5.15
4.96
5.14
5.54
5.22
Duke
5.31
4.89
5.09
5.57
5.36
4.71
5.13
5.30
Jersey
5.20
4.92
5.44
5.20
5.17
5.24
5.08
5.13
Sierra
5.08
5.30
5.43
4.99
4.89
5.30
5.35
5.26
a. We are to test whether the mean yields for all such bushes of the four varieties are the same.
Write the null and alternative hypotheses.
b. What are the degrees of freedom for the numerator and the denominator?
c. Calculate SSB, SSW, and SST.
d. Show the rejection and nonrejection regions on the F distribution curve for a = .01.
e. Calculate the between-samples and within-samples variances.
f. What is the critical value of F for a = .01?
g. What is the calculated value of the test statistic F?
h. Write the ANOVA table for this exercise.
i. Will you reject the null hypothesis stated in part a at a significance level of 1%?
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