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 a sample mean of x = 12.5%. Assume that x has a normal distribution and ó = 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 a = 0.05. (a) State the null and alternate hypotheses. Is this a left-tailed, right-tailed, or two-tailed test? (What answer below is correct?) H0: ? = 11%; H1: ? > 11%; right-tailed H0: ? = 11%; H1: ? ≠ 11%; two-tailed H0: ? ≠ 11%; H1: ? = 11%; two-tailed H0: ? = 11%; H1: ? < 11%; left-tailed (b) Compute the z 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. (d) Based on your answers in parts (a) to (c), what is the result of this hypothesis test? (Select the correct answer): We fail to reject the null hypothesis because the p-value is less than ? = 0.05. We reject the null hypothesis because the p-value is less than ? = 0.05. 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 greater than ? = 0.05. (e) State your conclusion in the context of the application. (Choose the right answer below.) There is sufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is different from 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 Colorado is less than 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 Colorado is greater than 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 Colorado is different from the national average
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 a sample mean of x = 12.5%. Assume that x has a
(b) Compute the z 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.
(d) Based on your answers in parts (a) to (c), what is the result of this hypothesis test? (Select the correct answer):
We fail to reject the null hypothesis because the p-value is less than ? = 0.05.
We reject the null hypothesis because the p-value is less than ? = 0.05.
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 greater than ? = 0.05.
(e) State your conclusion in the context of the application. (Choose the right answer below.)
There is sufficient evidence at the 0.05 level to conclude that the average hail damage to wheat crops in the county in Colorado is different from 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 Colorado is less than 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 Colorado is greater than 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 Colorado is different from the national average.
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