31) Most soybeans grown in the United States are genetically modified to, for ex

Question

31) Most soybeans grown in the United States are genetically modified to, for example, resist pests and so reduce 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 shipments of soybeans containing 1% of GM beans to 23 randomly selected facilities. Eighteen detected the GM beans.20

(a) Show that the conditions for the large-sample confidence interval are not met. Show that the conditions for the plus four interval are met.

(b) Use the plus four method to give a 90% confidence interval for the percent of all grain-handling facilities that will correctly detect 1% of GM beans in a shipment.

Explanation / Answer

(a)

The number of facilities detected the GM beans = 18

The number of facilities not detected the GM beans = 23-18 = 5

We see that number of succes is greater than 15 but number of failure is not greater than 15.

Hence, the conditions for the large-sample confidence interval are not met.

The conditions for use of the large-sample interval are not met because there

are only 5 failures. To apply the plus four method, we need to have atleast 5 sample size which is present in both the sample. Thus, plus four interval are met.

(b)

P = 18/23 = 0.7826

Z(0.1/2) = 1.645

90% confidence interval :

( 0.7826-1.645*sqrt( 0.7826*(1- 0.7826)/23), 0.7826+1.645*sqrt( 0.7826*(1- 0.7826)/23))

=( 0.6411178,0.9240822)

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.