Problem

Two different types of juice extractor, machine X and machine Y, are being compared. The manufacturer claims that machine Y extracts more juice per orange on average than machine X.

A random sample of 20 oranges is selected and each carefully measured. Oranges of a similar size and mass are then paired and numbered from 1 to 10. One orange from each pair is randomly allocated to machine X with the other allocated to machine Y. The amount of juice, in ml, extracted from each orange is recorded in the following table.

pair	1	2	3	4	5	6	7	8	9	10
machine X	65	73	58	61	72	79	64	65	69	71
machine Y	68	72	64	63	75	82	63	63	72	74

(a) Use a t-test to test the manufacturer’s claim at the $1\%$ significance level.

(b) State an assumption required for the test in 3(a) to be valid.

The manufacturer notices that the amount of juice extracted from the oranges in pair 4 were recorded incorrectly. In fact, the amount of juice extracted from machine X was $60\text{ ml}$ and from machine Y was $62\text{ ml}$.

(c) Explain, with justification, whether the conclusion of the test in 3(a) remains the same.