Question

The rust mite, a major pest of citrus in Florida, punctures the cells of leaves and fruit. Damage by rust mites is readily recognizable because the injured fruit displays a brownish (rust) color and is somewhat reduced in size depending on the severity of the attack. If the rust mites are not controlled, the affected groves have a substantial reduction in both the fruit yield and the fruit quality. In either case, the citrus grower suffers financially because the produce is of a lower grade and sells for less on the fresh-fruit market. This year, more and more citrus growers have gone to a program of preventive maintenance spraying for rust mites. In evaluating the effectiveness of the program, a random sample of fifty 10-acre plots, one plot from each of 50 groves, is selected. These show an average yield of 700 boxes of fruit, and the sample standard deviation was 70 boxes.

a) Construct a 95% confidence interval for ?, the average (10-acre) yield for all groves utilizing such a maintenance spraying program.

b) Interpret your confidence interval in one or two sentences without using the word “confident’’.

c) Using the same data, we want to construct a 99% confidence interval. Without performing the actual calculations, is the 99% confidence interval wider or narrower than the 95% confidence interval? Explain your answer in one sentence.

d) Suppose that we wanted to test ?0: ? = 725 boxes of fruit against the alternative hypothesis ?!: ? ≠ 725 with type I error rate ? = 0.05. Would we reject ?0 or fail to reject ?0 using the above data? Explain your reasoning in one sentence.

Answer 1