The average yield of the standard variety off soybeans per acreon a farm in a region is 48.8 bushels per acre, with a standarddeviation of 12.0 bushels per acre. We have developed a new varietyof soybean that we believe will have a higher mean yield per acre.To test this, we draw a random sample of 36 one-acre plots from theregion, plant the new variety of soybean, and compute the samplemean yield per acre. The sample mean yield per acre is 53.4bushels. Carry out the test at the 0.01 level of significance. (Youcan assume that yields per acre are approximately normallydistributed.) Follow all steps clearly and write a clearconclusion. Include all necessary conditions check and show allyour working.
Solved 1 Answer
See More Answers for FREE
Enhance your learning with StudyX
Receive support from our dedicated community users and experts
See up to 20 answers per week for free
Experience reliable customer service
Answer #1Let X be the average yield ofsoyabean      μ = 48.8 Population Mean     σ = 12 Population StandardDeviation     X̅ = 53.4 Sample Mean     n = 36 Sample Size     Let α = 0.01 Level ofsignificance     Since population standard deviation is known, we use thez-test      The null and alternative hypothesisare      Ho : μ = 48.8      H1 : μ > 48.8             Find Calculated Value of test statisticz      z=\frac{(\overline{\mathrm{x}}-\mu)}{\sigma / \sqrt{n}} \quad=\frac{(53.4-48.8)}{\frac{12}{\sqrt{36}}}=2.3z-score =2.3      This is a right sidedz-test      p-value for the test is found using Excel functionNORM.S.DIST      p-value = 1-NORM.S.DIST(2.3,TRUE)         (For rightsided test, subtract from 1)p-value =0.0107             Interpretation of p-value      Since 0.0107 >0.01                                  (p-value is marginally higher than significancelevel)    that is p-value > α      we DO NOT rejectHo             Conclusion :      There does not exist sufficient statisticalevidence to conclude that      new variety of soybean will have a higher mean yield peracre             (x- μ) (53.4-48.8) 12 oWn V36 ...