Zainab, the MSc student researching body length of bees from Question 4, continues analysing her data. The means and standard deviations of her random samples of bees from two different locations on the Isle of Wight are given in Table 5. Table 5 Location Sample size Mean length (cm) Standard deviation (cm) Yarmouth 1.33 0.08 Bembridge 1.32 0.09 (a) (i) Using the 1-Sample Z... option in Minitab, calculate and report a 95% confidence interval for the population mean length of bees from the Yarmouth area. In addition, include a copy of the Minitab output in your answer. (ii) Fill in the blanks in the following paragraph to interpret the ations) confidence interval that you have just calculated, in terms of all possible random samples of bees from the Yarmouth area. About of the possible random samples we could select will give rise to an interval containing the population while only about of the possible random samples we could select will give rise to an interval that does not contain the population (iii) On the basis of the confidence interval from part (a) (ii), what would have been the outcome of a z-test of the null hypothesis that the population mean length of bees from the Yarmouth area was 1.34 cm? Interpret the result of the test. (b) Now we want to compare the mean lengths of bees between the two regions given in Table 5 Interest now centres on the difference between body lengths of bees in the Yarmouth and the Bembridge regions. (i) Calculate by hand the value of the estimated standard error of the difference between the sample means. (ii) Calculate by hand a 95% confidence interval for the difference between the population mean lengths of bees in the Yarmouth and the Bembridge regions. (iii) On the basis of the confidence interval from part (b) (ii), what would have been the outcome of a z-test of the null hypothesis that the population mean length of bees in the Yarmouth region was the same as the population mean lengths of bees in the Bembridge region? Interpret the result of the test