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Wormy fruit trees. It is generally thought that the percentage of fruit attacked by codling moth larvae is greater on apple trees bearing a small crop. Apparently the density of the flying moths is unrelated to the size of the crop on a tree, so the chance of attack for any particular fruit is increased if few fruits are on the tree.

Data collected for a random sample of 10 trees gives a sample linear correlation coefficient of -0.8. Other summary statistics obtained from the sample are provided below.

variable sample mean sample stand dev
corp size (#of fruit) 110 40
% of wormy fruits 45 12

Write down the ANOVA table for the simple linear regression of percentage of wormy fruit on crop size. Compute the F statistic and find a p-value. Find a 99% confidence interval for B1, the slope of the least squares regression line for predicting the percentage of wormy fruit from crop size. What proportion of the variability in the percentage of wormy fruit is explained by the regression of percentage of wormy fruit on crop size? Estimate the mean percentage of wormy fruits for trees with a crop size of 150 fruit. Provide a 95% confidence interval for the mean percentage of wormy fruits for trees with a crop size of 150 fruit. Is there statistically significant evidence from these data that trees with a crop size of 150 have, on average, 50% wormy fruit? Provide a 90% prediction interval for the average percentage of wormy fruit for the first tree with 150 fruit that was selected to be part of the study.