Question 4 (Unit 7) - 10 marks You will need to use Minitab to answer this question. For her MSc dissertation in Biology, Zainab compares some recently discovered wild bee colonies near Yarmouth on the Isle of Wight with the common wild bee species found in the New Forest in mainland Hampshire. One way in which she is comparing the bee populations is through the body size (length in centimetres) of individual bees, which she can measure through an app on her phone. The population mean length of the New Forest species is known to be 1.3 cm, and Zainab measures a random sample of bees on the Isle of Wight. The sample size, mean and standard deviation for the Isle of Wight bees are presented in Table 3. Table 3 Sample size Mean length (cm) Standard deviation (cm) 36 1.33 0.08 A one-sample 2-test is to be performed to investigate whether the population mean length of a bee on the Isle of Wight is the same as the population mean length of the New Forest species of bee. (a) Using appropriate notation, which you should define, specify the null and alternative hypotheses associated with the test. [2] (b) Use Minitab to perform a one-sample z-test on the bee data. Include a copy of the relevant Minitab output in your answer. What is the value of the test statistic? [3] (c) Give the p-value from the test performed in part (b), and say what may be concluded from the test in terms of evidence about the hypotheses. Relate your conclusions back to consideration of the population mean length of bees on the Isle of Wight. [3] (d) Suppose that Zainab discovers further bee colonies near Bembridge on the other side of the Isle of Wight. She obtains a sample of size 42 of lengths from these bees. She proposes to use a two-sample 2-test to make an appropriate comparison regarding the lengths of the two populations found in different locations, Yarmouth and Bembridge, on the Isle of Wight. Using appropriate notation, which you should define, specify the mill and alternative hypotheses that would be associated with this test. [2]