Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.t An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 14 7 10 11 12 19 14 11 9 8 23 19 13 10 The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and a = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 11%; H,: u < 11%; left-tailed O Ho: H = 11%; H,: u > 11%; right-tailed O Ho: H+ 11%; H,: µ = 11%; two-tailed O Ho: H = 11%; H,: u+ 11%; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since n is large with unknown a. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, since we assume that x has a normal distribution with known a. O The standard normal, since we assume that x has a normal distribution with known o. Compute the z value of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.t An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 14 7 10 11 12 19 14 11 9 8 23 19 13 10 The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and a = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 11%; H,: u < 11%; left-tailed O Ho: H = 11%; H,: u > 11%; right-tailed O Ho: H+ 11%; H,: µ = 11%; two-tailed O Ho: H = 11%; H,: u+ 11%; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since n is large with unknown a. O The standard normal, since we assume that x has a normal distribution with unknown a. O The Student's t, since we assume that x has a normal distribution with known a. O The standard normal, since we assume that x has a normal distribution with known o. Compute the z value of the sample test statistic. (Round your answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.t An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in
the county reported the percentage of their wheat lost to hail.
14 7
10 11 12
19 14 11
9 8 23
19 13 7
10 7
The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and a = 5.0%. Do these data
indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use a = 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
O Ho: H = 11%; H,: µ < 11%; left-tailed
O Ho: u = 11%; H,: µ > 11%; right-tailed
O Ho: H + 11%; H,: u = 11%; two-tailed
O Ho: H = 11%; H,: u + 11%; two-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The Student's t, since n is large with unknown a.
The standard normal, since we assume that x has a normal distribution with unknown o.
O The Student's t, since we assume that x has a normal distribution with known o.
O The standard normal, since we assume that x has a normal distribution with known o.
Compute the z value of the sample test statistic. (Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
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