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. 13 8 9 11 13 20 12 12 6 8 22 19 12 11 13 7 The sample mean is x = 12.3%. 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 o = 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 Hoi u= 11%; H,: u< 11%; left-tailed O Hoi u 11%: H: u = 11%% two-tailed O H,i u= 11%b; H,: u# 11%; two-tailed O H,: u = 11%; H, : u > 11%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since we assume that x has a normal distribution with known a. O The Student's t, since n is large with unknown o. O The standard normal, 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 unknown a. 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. 13 8 9 11 13 20 12 12 6 8 22 19 12 11 13 7 The sample mean is x = 12.3%. 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 o = 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 Hoi u= 11%; H,: u< 11%; left-tailed O Hoi u 11%: H: u = 11%% two-tailed O H,i u= 11%b; H,: u# 11%; two-tailed O H,: u = 11%; H, : u > 11%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since we assume that x has a normal distribution with known a. O The Student's t, since n is large with unknown o. O The standard normal, 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 unknown a. 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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Transcribed Image Text: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.
13 8
9 11 13 20 12 12
6 8 22 19 12 11 13 7
The sample mean is x = 12.3%. 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 o = 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 Hoi u= 11%; H,: u< 11%; left-tailed
O Hoi u 11%: H: u = 11%% two-tailed
O H,i u= 11%b; H,: u# 11%; two-tailed
O H,: u = 11%; H, : u > 11%; right-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
O The Student's t, since we assume that x has a normal distribution with known a.
O The Student's t, since n is large with unknown o.
O The standard normal, 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 unknown a.
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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