In 2011, the average yield (bushels per acro) of organic wheat farms was lower t

Question

In 2011, the average yield (bushels per acro) of organic wheat farms was lower than that of conventional farms (McBride and Greone, 2015). Supposo Diego, an agricultural researcher, wanled to determine if the wheat yicld in 2015 showed the same trend. He sclected 40 organic wheal farms and 40 conventional whcat farms at random and acquired data on the 2015 wheat yield for each farm. The table presents his summary data Samplemean n,-40i-3727 na = 40 , = 45, 13 PopulationPopulation Sample Sample descriptionsize Sample standard deviation 51 = 16.32 52 = 18.98 Organic Conventional Diego's daa set did not contain any outlicrs, so he ran a two-samplc ftest for independent samplcs with unknown population standard deviations a1 a significance level of -0.05·The lable shows the results of his lcsL Sample means Degrees of freedom (approximate) df 39 Statistic Probability 7.86 -1.9859 0.0271 Complctc the following sentences to state Dicgo's decision and conclusion. the at a signilicance level Dicgo of = 0.05. There is | evidence to conclude that the avcrage yield of the average yicld of Anawer Bank null typothesis surmpio sine the same a the conventional wheat farms in his sample let stalistic the urpanic wheal farins in hes sample acceptsa all conveniional wheal faras

Explanation / Answer

Given that,
mean(x)=37.27
standard deviation , s.d1=16.32
number(n1)=40
y(mean)=45.13
standard deviation, s.d2 =18.98
number(n2)=40
null, Ho: u1 > u2
alternate, H1: u1 < u2
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.685
since our test is left-tailed
reject Ho, if to < -1.685
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =37.27-45.13/sqrt((266.3424/40)+(360.2404/40))
to =-1.9859
| to | =1.9859
critical value
the value of |t | with min (n1-1, n2-1) i.e 39 d.f is 1.685
we got |to| = 1.98593 & | t | = 1.685
make decision
hence value of | to | > | t | and here we reject Ho
p-value:left tail - Ha : ( p < -1.9859 ) = 0.02705
hence value of p0.05 > 0.02705,here we reject Ho
ANSWERS
---------------
null, Ho: u1 = u2
alternate, H1: u1 < u2
test statistic: -1.9859
critical value: -1.685
decision: reject Ho
p-value: 0.02705

Diego reject the null hypothesis at a significnac level f alpha 0.05. there is
suffcient evidence to conlcude that the average yield of the organix wheat farms in his sample is less than the average yield of all conventional wheat farms

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