On 3rd March, 1991, the glass window at the front of a pharmacy in Hamilton, New Zealand was smashed, and thousands of dollars' worth of goods and prescription medicines were stolen. The police subsequently apprehended two suspects. Glass fragments were found in the clothing of one suspect. The refractive index (RI) of each piece, and the RIs of small pieces of glass subsequently taken from the remnants of the window, and the data are below.

Suspect Window

1.5194 1.5195

1.51946 1.51952

1.51947 1.51953

1.51948 1.51956

1.5195 1.51957

1.51952 1.51959

1.51952 1.5196

1.51953 1.5196

1.51956 1.51962

1.51957 1.51964

1.51957

a) Show the data in a structure that allows it to be readily analysed using R Commander.

b) State the null and alternative hypotheses (i.e. H0 and H1) that you will test by writing s and w for the mean RIs of the populations from which the samples of glass on the suspect's clothing and from the window came. Explain why you chose H0 and H1 in the way that you did (e.g., why did you choose a hypothesis to be H0 and not H1?)

c) It is proposed to perform a pooled t-test at the 5% level of significance on the data. State all assumptions that this test makes about the data that are in the two samples.

d) Check whether the assumptions specified in part c) are satisfied. State your conclusions clearly. You can produce and use R Commander output to support your conclusions.

e) Use an appropriate test to test the hypotheses specified in part b). Use R Commander to perform this test