# Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail. An insurance

## 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 Weld County, Colorado. A random sample of 16 claims in Weld County gave the following data (% wheat crop lost to hail):

The sample mean is = 12.5%. Let x be a random variable that represents the percentage of wheat crop in Weld County lost to hail. Assume that x has a normal distribution and Ïƒ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in Weld County is different (either way) from the national mean of 11%? Use Î± = 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?
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the value of the sample test statistic.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)€“(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level Î±?
(e) Interpret your conclusion in the context of the application.

Distribution
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