A bioengineering firm was working to increase the yield of eggplant crops, and it developed two promising strains of eggplant. In early tests, Strain A appeared to produce a slightly smaller yield than Strain B, but the difference was too small to be significant. The company decided to check that Strain A produced less than Strain B by replicating the test on a much larger scale by planting the crops in 15 different fields. The fields were randomly assigned a density at which the seeds were planted, with half of each field growing one of the two strains of eggplant.
The firm tests the paired data, where α=0.05, in order to evaluate the claim that the true mean difference between the yield of Strain A and the yield of Strain B is less than zero.
(a) Which answer choice shows the correct null and alternative hypotheses for this test?
Select the correct answer below:
H0:μd=0; Ha:μd>0, which is a right-tailed test.
H0:μd=0, Ha:μd≠0, which is a two-tailed test.
H0:μd=0, Ha:μd<0, which is a left-tailed test.
H0:μd≠0, Ha:μd=0, which is a two-tailed test.
Answer :
H0:μd=0, Ha:μd<0, which is a left-tailed test.
Explanation : In example we have claim that the true mean difference(μd) between the yield of Strain A and the yield of Strain B is less than zero. That means it is inequality hence option 2&4 are incorrect.
From remaining 1&3 we require less than inequality in alternative hypothesis. That is given in option 3.(Correct)
option 1 is also incorrect.
NOTE: generally in very most of the cases the null hypothesis is of eqaulity type ( i.e H0: μd=0).
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