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Numerade Educator

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Problem 140 Hard Difficulty

A commercial farmer harvests his entire field of a vegetable crop at one time. Therefore, he would like to plant a variety of green beans that mature all at one time (small standard deviation between maturity times of individual plants). A seed company has developed a new hybrid strain of green beans that it believes to be better for the commercial farmer. The maturity time of the standard variety has an average of 50 days and a standard deviation of 2.1 days. A random sample of 30 plants of the new hybrid showed a standard deviation of 1.65 days. Does this sample show a significant lowering of the standard deviation at the 0.05 level of significance? Assume that maturity time is normally distributed.
a. Solve using the $p$ -value approach.
b. Solve using the classical approach.

Answer

a. $p$ - value is greater than $\alpha,$ hence fail to reject the null hypothesis $H_{0}$.
b. left hand tail because $H$. expresses concern values related to less than.
c. $\chi^{2}$ is not in the critical region, hence fail to reject the null hypothesis $H_{0}$.

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Video Transcript

Hi. This question We get sample size equal to Terry. So did me. Freedom is 29. Megan Alfa has went or pipe and we get our alternative Sigma Lis ban to want one. And our sample standard deviation is 1.65 So I use the formula for the test statistics on Find that that the battle is 17 Boardman three. And when I tried to find the value here in the table, As you can see here, we don't have the valuable do freedom off 29. So you have to make some population between 28 Terry on. I'm guessing that the value is a little off 0.95 which is equivalent to ah p value off point or five eso We come up with the conclusion fail to reject. Honestly, it is a little bit difficult to find that table. So I do recommend, um, everyone toe he was one of the software of calculator toe to find the p value or that chi square clinical value. So it can be on one more thing. No notes that we have a list down here. So we are on the left tail case. Something like that. Thank you.