A severe tornado recently touched down in Bryce County, Kansas. Government policy calls for emergency support if the average damage done to the population of all farms in the county exceeds $ 20,000. At the moment, the government is not at all convinced that this criterion has been met. To demonstrate that average damage is more than the $ 20,000 figure, you audit a simple random sample of 40 farms in the county and find that the average damage for the farms in the sample is $ 21,100. Should this be considered sufficient sample evidence to convince a reluctant government agency to provide the emergency support? That is, is this sufficient evidence to reject a “μ is no more than $ 20,000” null hypothesis in favor of a “μ is greater than $ 20,000” alternative? To make your decision, determine the critical value for the test in $ and compare the sample mean to the critical value. Use a significance level of 5%. Assume the population standard deviation is $ 3700.
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