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,t 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 17 87 10 14 19 16 12 7 9 26 20 14 8 10 3 The sample mean is x = 12.5%. 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 ? 5.096. 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 1190? Use -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? O Ho : ? 1 196, H1 : ?- 1196 ; two-tailed Ho : ?-11%; H1 : ? > 11%; right-tailed Ho : ?-11%; H1 : ? # 11%; two-tailed Ho : ?-11%; H1 : ?

Explanation / Answer

The statistical software output for this problem is:

One sample Z hypothesis test:
? : Mean of variable
H0 : ? = 11
HA : ? ? 11
Standard deviation = 5

Hypothesis test results:

Hence,

a) Level of significance = 0.01

Sample test statistic = 1.2

P - value = 0.2301

Variable n Sample Mean Std. Err. Z-Stat P-value Data 16 12.5 1.25 1.2 0.2301

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