Most soybeans grown in the United States are genetically modified to, for exampl

Question

Most soybeans grown in the United States are genetically modified to, for example, resist pests and so reduce the use of pesticides. Because some nations do not accept genetically modified (GM) foods, grain-handling facilities routinely test soybean shipments for the presence of GM beans. In a study of the accuracy of these tests, researchers submitted lots of soybeans containing 1 % of GM beans to 23 randomly selected facilities. 18 detected the GM beans.   

(a) Explain why the conditions to use the normal approximation are not satisfied. Use Stata to find the Wilson 90 % confidence interval for the percent of all grain-handling facilities that would correctly detect the presence of 1% GM beans in a shipment. Paste your Stata Results here:

(b) Write a summary sentence, interpreting the 90 % confidence interval for an audience of soybean growers and exporters.

Explanation / Answer

Answer:

Most soybeans grown in the United States are genetically modified to, for example, resist pests and so reduce the use of pesticides. Because some nations do not accept genetically modified (GM) foods, grain-handling facilities routinely test soybean shipments for the presence of GM beans. In a study of the accuracy of these tests, researchers submitted lots of soybeans containing 1 % of GM beans to 23 randomly selected facilities. 18 detected the GM beans.   

(a) Explain why the conditions to use the normal approximation are not satisfied. Use Stata to find the Wilson 90 % confidence interval for the percent of all grain-handling facilities that would correctly detect the presence of 1% GM beans in a shipment. Paste your Stata Results here:

ci var1 [fweight = var2], binomial wilson level(90)

                                                         ------ Wilson ------

    Variable |        Obs        Mean   Std. Err.       [90% Conf. Interval]

-------------+---------------------------------------------------------------

        var1 |         23    .7826087    .0860061        .6157819    .8899455

90% CI for proprtion = (0.6158, 0.8899)

90% CI for percentage = (61.58, 88.99)

(b) Write a summary sentence, interpreting the 90 % confidence interval for an audience of soybean growers and exporters.

We are 90 % confidence interval for all audience of soybean growers and exporters % detected the GM bean falls between ( 61.58% to 88.99%).

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