Researchers are planning a study to estimate the impact on crop yield when no-till is used in combination with residue retention and crop rotation. Based on data from a meta-analysis of 610 small farms, the researchers estimate there is a 2.5% decline in crop yield when no-till is used with residue retention and crop rotation. Suppose the researchers want to produce a 95% confidence interval with a margin of error of no more than 1.0%. Determine the minimum sample size requiblack for this study. The sample size needed to create a confidence interval estimate depends on the margin of error, the initial estimated proportion, and the confidence level. Be sure to use proportions rather than percentages. Round your final answer up to the nearest whole number. n = ◻ field comparisonsSuppose that administrators of a large school district wish to estimate the proportion of children in the district enrolling in kindergarten who attended preschool. They took a simple random sample of children in the district who are enrolling in kindergarten. Out of 60 children sampled, 42 had attended preschool. Construct a large-sample 99% z-confidence interval for p, the proportion of all children enrolled in kindergarten who attended preschool. Give the limits of the confidence interval as decimals, precise to at least three decimal places. lower limit : upper limit : Construct a plus four 99% z-confidence interval for p. Give the limits of the confidence interval as decimals, precise to at least three decimal places. lower limit : upper limit :

Question

Researchers are planning a study to estimate the impact on crop yield when no-till is used in combination with residue retention and crop rotation. Based on data from a meta-analysis of 610 small farms, the researchers estimate there is a 2.5% decline in crop yield when no-till is used with residue retention and crop rotation. Suppose the researchers want to produce a 95% confidence interval with a margin of error of no more than 1.0%. Determine the minimum sample size requiblack for this study. The sample size needed to create a confidence interval estimate depends on the margin of error, the initial estimated proportion, and the confidence level. Be sure to use proportions rather than percentages. Round your final answer up to the nearest whole number. n =   ◻     field comparisonsSuppose that administrators of a large school district wish to estimate the proportion of children in the district enrolling in kindergarten who attended preschool. They took a simple random sample of children in the district who are enrolling in kindergarten. Out of 60 children sampled, 42 had attended preschool. Construct a large-sample 99% z-confidence interval for p, the proportion of all children enrolled in kindergarten who attended preschool. Give the limits of the confidence interval as decimals, precise to at least three decimal places. lower limit : upper limit : Construct a plus four 99% z-confidence interval for p. Give the limits of the confidence interval as decimals, precise to at least three decimal places. lower limit : upper limit :

Rose Holmes · Accepted Answer

From the provided information,Confidence level = 95%Margin of error (  E) = 1.0% that is 0.01Sample proportion (            p      ^      ) = 2.5% or 0.025The   z value at 95% confidence level from the standard normal table is 1.96.The requiblack sample size can be obtained as:  n  =            p      ^        (  1  −            p      ^        )  (            z              α                  /                2              E        )    2      =  (  0.025  )  (  1  −  0.025  )  (      1.96    0.01        )    2      =  936.39    ≈  937Thus, the requiblack sample size is 937.

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