Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail. An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported a sample mean of x = 12.8%. 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 = 0.05. (a) State the null and alternate hypotheses. Is this a left-tailed, right-tailed, or two-tailed test? Ho: H = 11%; H₁: > 11%; right-tailed O Ho: H= 11%; H₁: 11% ; two-tailed O Ho: H= 11%; H₁: < 11%; left-tailed O Ho: 11%; H₁: = 11%; two-tailed (b) 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. (d) Based on your answers in parts (a) to (c), what is the result of this hypothesis test? O we fail to reject the null hypothesis because the p-value is less than a = 0.05. O We fail to reject the null hypothesis because the p-value is greater than a = 0.05. O We reject the null hypothesis because the p-value is less than a = 0.05. O We reject the null hypothesis because the p-value is greater than a = 0.05. (e) State your conclusion in the context of the application. O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is different from the national average. O There is sufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is different from the national average. O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is greater than the national average. O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is less than the national average.
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail. An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported a sample mean of x = 12.8%. 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 = 0.05. (a) State the null and alternate hypotheses. Is this a left-tailed, right-tailed, or two-tailed test? Ho: H = 11%; H₁: > 11%; right-tailed O Ho: H= 11%; H₁: 11% ; two-tailed O Ho: H= 11%; H₁: < 11%; left-tailed O Ho: 11%; H₁: = 11%; two-tailed (b) 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. (d) Based on your answers in parts (a) to (c), what is the result of this hypothesis test? O we fail to reject the null hypothesis because the p-value is less than a = 0.05. O We fail to reject the null hypothesis because the p-value is greater than a = 0.05. O We reject the null hypothesis because the p-value is less than a = 0.05. O We reject the null hypothesis because the p-value is greater than a = 0.05. (e) State your conclusion in the context of the application. O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is different from the national average. O There is sufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is different from the national average. O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is greater than the national average. O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is less than the national average.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail. An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in
the county reported a sample mean of x = 12.8%. 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 = 0.05.
(a) State the null and alternate hypotheses. Is this a left-tailed, right-tailed, or two-tailed test?
Ho: M = 11%; H₁: μ> 11%; right-tailed
Ho: M = 11%; H₁: H 11%; two-tailed
O Ho: M = 11%; H₁: μ< 11%; left-tailed
Ho: M 11%; H₁: μ = 11%; two-tailed
(b) Compute the z value of the sample test statistic. Round your answer to two decimal places.
.... V
(c) Find (or estimate) the P-value. Round your answer to four decimal places.
(d) Based on your answers in parts (a) to (c), what is the result of this hypothesis test?
O We fail to reject the null hypothesis because the p-value is less than α = 0.05.
O We fail to reject the null hypothesis because the p-value is greater than α = 0.05.
O We reject the null hypothesis because the p-value is less than a = 0.05.
O We reject the null hypothesis because the p-value is greater than a = 0.05.
(e) State your conclusion in the context of the application.
O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is different from the national average.
O There is sufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is different from the national average.
O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is greater than the national average.
O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is less than the national average.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fb2db49-0d9a-48f5-a584-53a74d58c16a%2F2a99e877-b17b-4701-a01f-4e90117df75e%2Fcw850y_processed.png&w=3840&q=75)
Transcribed Image Text:Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail. An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in
the county reported a sample mean of x = 12.8%. 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 = 0.05.
(a) State the null and alternate hypotheses. Is this a left-tailed, right-tailed, or two-tailed test?
Ho: M = 11%; H₁: μ> 11%; right-tailed
Ho: M = 11%; H₁: H 11%; two-tailed
O Ho: M = 11%; H₁: μ< 11%; left-tailed
Ho: M 11%; H₁: μ = 11%; two-tailed
(b) Compute the z value of the sample test statistic. Round your answer to two decimal places.
.... V
(c) Find (or estimate) the P-value. Round your answer to four decimal places.
(d) Based on your answers in parts (a) to (c), what is the result of this hypothesis test?
O We fail to reject the null hypothesis because the p-value is less than α = 0.05.
O We fail to reject the null hypothesis because the p-value is greater than α = 0.05.
O We reject the null hypothesis because the p-value is less than a = 0.05.
O We reject the null hypothesis because the p-value is greater than a = 0.05.
(e) State your conclusion in the context of the application.
O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is different from the national average.
O There is sufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is different from the national average.
O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is greater than the national average.
O There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is less than the national average.
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