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.

17	9	8	13	10	19	14	9
8	8	26	22	11	9	12	7

The sample mean is x = 12.6%. 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 σ = 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 α = 0.01.

1) Compute the z value of the sample test statistic. (Round your answer to two decimal places.)
2) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 0.11

H_a : 0.11

Test statistic = z

= ( - ) / / n

= (0.126 - 0.11) / 0.05 / 16

Test statistic = 1.28

P(z > 1.28) = 1 - P(z < 1.28) = 0.1003

P-value = 0.2006