Chapter 9.1, Problem 23P

For Problems 19-24, please provide the following information.

(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) Check Requirements What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. Compute the z 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) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level $\alpha$?

(e) Interpret your conclusion in the context of the application.

Insurance: Hail Damage Nationally, about 11 % of the total U.S. wheat crop is destroyed each year by hail (Reference: Agricultural Statistics, U.S. Department of Agriculture). 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).

15	8	9	II	12	20	14	11
7	10	24	20	13	9	12	5

The sample mean is $\bar{x}$ = $12.5\%.$ 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 $\sigma =5.0\%$ 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 $\alpha =0.01$.