An agricultural researcher plants 25 plots with a new variety of yellow corn. As

Question

An agricultural researcher plants 25 plots with a new variety of yellow corn. Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with an unknown mean of mu and a standard deviation of sigma = 10 bushels per acre. If the average yield for these 25 plots is x = 150 bushels per acre, what is a 90% confidence interval for mu? 150 plusminus 0.784 150 plusminus 2.00 150 plusminus 3.29 150 plusminus 3.92 An agricultural researcher plants 25 plots with a new variety of yellow corn. Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with an unknown mean of mu and a standard deviation of sigma = 10 bushels per acre. Which of the following would produce a confidence interval with a smaller margin of error than the 90% confidence interval? Plant only five plots rather than 25 because five are easier to manage and control. Plant 10 plots rather than 25 because a smaller sample size will result in a smaller margin of error. Plant 100 plots rather than 25 because a larger sample size will result in a smaller margin of error. Compute a 99% confidence interval rather than a 90% confidence interval because a higher confidence level will result in a smaller margin of error. The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured. The sample mean is x = 66.2 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of sigma = 4.1 inches. Suppose the heights of a simple random sample of 100 male sophomores were measured rather than 400. Which of the following statements is true? The margin of error for the 95% confidence interval would increase. The margin of error for the 95% confidence interval would decrease. The margin of error for the 95% confidence interval would stay the same because the level of confidence has not changed. The standard deviation a would decrease.

Explanation / Answer

Z=1.96 for 95% confidence probability

Standard error = z*sigma/ Sqrt(n)= 1.96 * 10/5= 3.92

Hence,answer is D.

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