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 of16 claimsin the county reported a sample mean ofx= 12.3%. Assume thatxhas a normal distribution and= 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= 0.05.(a)

State the null and alternate hypotheses. Is this a left-tailed, right-tailed, or two-tailed test?

H₀:= 11%;H₁:< 11%; left-tailed

H₀:= 11%;H₁:11%; two-tailed

H₀:= 11%;H₁:> 11%; right-tailed

H₀:11%;H₁:= 11%; two-tailed

(b) Compute thezvalue of the sample test statistic.

(c) Find (or estimate) theP-value.

(d) Based on your answers in parts (a) to (c), what is the result of this hypothesis test?

We reject the null hypothesis because the p-value is greater than= 0.05.

We fail to reject the null hypothesis because the p-value is less than= 0.05.

We fail to reject the null hypothesis because the p-value is greater than= 0.05.

We reject the null hypothesis because the p-value is less than= 0.05.

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

There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Coloradois less thanthe national average.

There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Coloradois differentfrom the national average.

There is insufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Coloradois greater thanthe national average.

There is sufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Coloradois differentfrom the national average.