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.
13 6 10 13 12 20 16 9 7 8 25 18 15 9 14 6
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.
(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?
H0: μ = 11%;
H1: μ ≠ 11%; two-tailed
H0: μ = 11%;
H1: μ > 11%;
right-tailed
H0: μ ≠ 11%;
H1: μ = 11%; two-tailed
H0: μ = 11%;
H1: μ < 11%; left-tailed
(b) What sampling distribution will you use? Explain the rationale
for your choice of sampling distribution.
The standard normal, since we assume that x has a
normal distribution with known σ.
The Student's t, since we assume that x has a
normal distribution with known
σ.
The standard normal, since we assume that x has a
normal distribution with unknown σ.
The Student's t, since n is large with unknown
σ.
What is the value of the sample test statistic? (Round your
answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to
four decimal places.)