You are in charge of rural economic development in a rapidly developing country that is using its newfound oil wealth to develop the entire country. As part of your responsibility you have been asked to determine if there is evidence that the new rice-growing procedures have increased output per hectare. A random sample of 27 fields was planted using the old procedure, and the sample mean output was 60 per hectare with a sample variance of 100. During the second year the new procedure was applied to the same fields and the sample mean output was 64 per hectare, with a sample variance of 150. The sample correlation between the two fields was 0.38. The population variances are assumed to be equal, and that assumption should be used for the problem analysis.
a. Use a hypothesis test with a probability of Type I error = 0.05 to determine if there is strong evidence to support the conclusion that the new process leads to higher output per hectare, and interpret the results.
b. Under the assumption that the population variances are equal, construct a 95% acceptance interval for the ratio of the sample variances. Do the observed sample variances lead us to conclude that the population variances are the same? Please explain.