Q2) Researchers at a paint manufacturer are trying to develop a new type of gloss paint with a shorter drying time than the current product. In order to test whether the drying time has been reduced, the researchers paint a square metre of each of the new and old paints on each of 10 different surfaces. The time, in hours, that each square metre takes to dry is recorded in the table below: Surface 1 2 3 4 5 6 7 8 9 10 Old paint 17.1 17.3 16.9 17.4 17.5 17.3 16.6 17.5 18.0 17.6 New paint 16.6 17.2 17.0 17.1 17.6 16.5 16.9 17.3 17.3 16.9 (a) Test, at the 0.05 level of significance, whether there is any reduction in the mean drying time. (b) State the assumption required to carry out the test in (a). (c) Find the p-value of the test in (a). (?? Marks)

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Chapter1: Combinatorial Analysis
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Q2)
Researchers at a paint manufacturer are trying to develop a new type of gloss paint with a shorter
drying time than the current product. In order to test whether the drying time has been reduced,
the researchers paint a square metre of each of the new and old paints on each of 10 different
surfaces. The time, in hours, that each square metre takes to dry is recorded in the table below:
Surface
1
2
3
4
5 6
7 8 9
10
Old paint
17.1 17.3 16.9 17.4 17.5 17.3 16.6 17.5 18.0 17.6
New paint
16.6 17.2 17.0 17.1 17.6 16.5 16.9 17.3 17.3 16.9
(a) Test, at the 0.05 level of significance, whether there is any reduction in the mean drying time.
(b) State the assumption required to carry out the test in (a).
(c) Find the p-value of the test in (a).
(?? Marks)
Transcribed Image Text:Q2) Researchers at a paint manufacturer are trying to develop a new type of gloss paint with a shorter drying time than the current product. In order to test whether the drying time has been reduced, the researchers paint a square metre of each of the new and old paints on each of 10 different surfaces. The time, in hours, that each square metre takes to dry is recorded in the table below: Surface 1 2 3 4 5 6 7 8 9 10 Old paint 17.1 17.3 16.9 17.4 17.5 17.3 16.6 17.5 18.0 17.6 New paint 16.6 17.2 17.0 17.1 17.6 16.5 16.9 17.3 17.3 16.9 (a) Test, at the 0.05 level of significance, whether there is any reduction in the mean drying time. (b) State the assumption required to carry out the test in (a). (c) Find the p-value of the test in (a). (?? Marks)
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