Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hai

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 claimsin the county reported the percentage of their wheat lost to hail.

The sample mean is x = 11.9%. 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 (either way) from the national mean of 11%? Use = 0.01.

a. Compute the z value of the sample test statistic? (Round your answer to two decimal places.)


b. Find (or estimate) the P-value. (Round your answer to four decimal places.)

Explanation / Answer

Standard error, SE = /sqrt(n) = 5/sqrt(16) = 1.25

Z = (x-mean)/SE = (11.9 - 11)/1.25 = 0.72

p-value(two tailed) = 0.4715 > 0.01, fail to reject the null hypothesis

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