(a) A random sample of 500 residents was selected from a local council's record and it was found that 15 of these residents had been born in New Zealand. Calculate a 95 % confidence interval to estimate the proportion of all residents in the local council area who had been born in New Zealand.

(b) Is the average marks between the Literacy tests and Numeracy Test the same?

A sample of 26 students in Literacy and Numeracy marks were matched to answer the research question above. The same 26 students sat both the Literacy and the Numeracy test and a statistical test was carried out to find whether there is any difference between average marks of the two tests. The sample mean difference was 11.675 and the sample standard deviation was 7.298

Use the following information and answer the above research question at 5% level of significance.