Answered: Nationally, about 11% of the total U.S.…

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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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 the percentage of their wheat lost to hail.

16	6	8	11	13	20	12	13
7	8	26	19	13	7	10	3

The sample mean is x = 12.000%. 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 ? = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different from the national mean of 11%? Use ? = 0.01.

(a) What is the level of significance?

State the null hypothesis

H₀

and the alternate hypothesis

H₁

H₀

: ?

H₁

: ?

What kind of test is this?

right-tailed testtwo-tailed test left-tailed test

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The standard normal, since we assume that x has a normal distribution with known ?.The Student's t, since n is small with unknown ?.

Compute the sample test statistic based on your choice of the distribution. (Round your answer to two decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in the previous parts, state your decision. Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) State your conclusion.

There is sufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average.There is insufficient evidence at the 0.01 level to conclude that the average hail damage to wheat crops in the county in Colorado differs from the national average

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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