Historically, about 12% of Canada's wheat crop is destroyed by hail, every year. An insurance company is studying damage to wheat crops in parts of Saskatchewan. A random sample of 10 claims from the region gave the following percentages of wheat lost to hail damage.

13 10 15 13 22 14 11 18 16 10

a) If we can assume that the percentage of crop damage due to hail is normally distributed with a [10] standard deviation of 3%, conduct a full hypothesis test to determine if the insurance claims reflect a significant increase over previous years at a significance level of 0.05.

The test must include: The null and alternate hypotheses, the type of test, the test statistic, the p-value, a decision and a conclusion in the context of the situation. Use the p-value approach.

(b) If the standard deviation for the population is not known, but we can assume that the population is normally distributed, construct a 95% confidence interval for the mean percentage of wheat damage due to hail. Interpret the result.

(c_If the standard deviation for the population is not known, and we can assume that the population is normally distributed, conduct a full hypothesis test to determine if the insurance claims for this year reflect a difference from previous years at a significance level of = 0.05. The test must include the null and alternate hypotheses, the type of test, the test statistic, the critical value from the appropriate distribution, a decision and a conclusion in the context of the situation. Use the critical value approach and sketch a curve showing the areas involved in the test.