4 2 Mohamed grows courgettes on his farm. He knows that the weights, in grams, of courgettes grown on other nearby farms are distributed N(175, 22.0 2). Mohamed decides to compare the weight of courgettes grown on his farm with the weight of courgettes grown on other nearby farms. Mohamed takes a random sample of 16 courgettes grown on his farm. The mean weight of courgettes in this random sample is 182.9 grams. (a) Calculate a 95% confidence interval for the mean weight of courgettes grown on Mohamed’s farm. You may assume that the standard deviation of weights of courgettes grown on Mohamed’s farm is the same as that for courgettes grown on other nearby farms. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (b) Explain why the confidence interval you calculated in (a) does not provide significant evidence that courgettes grown on Mohamed’s farm have a mean weight different from 175 grams. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________