Question 5 (12 Marks) The following measurements were recorded by a paint manufa

Question

Question 5 (12 Marks) The following measurements were recorded by a paint manufacturer for the drying time, in hours, of a certain brand of latex paint: 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 2.8 4.4 4 5.2 3 4.8 a) Compute the probability distribution of this population b) By assuming that the measurements represent a random sample from a normal population. find a point estimate for the true mean drying time of the paint. c) Construct a 95% confidence interval for the drying time for the next trial of all latex paint.

Explanation / Answer

A) mean = (3.4 + 2.8 + 4.4 + 2.5 + 3.3 + 4 + 4.8 + 5.6 + 5.2 + 2.9 + 3.7 + 3 + 3.6 + 2.8 + 4.8)/15 = 3.787

Variance = ((3.4 - 3.787)^2 + (2.8 - 3.787)^2 + (4.4 - 3.787)^2 + (2.5 - 3.787)^2 + (3.3 - 3.787)^2 + (4 - 3.787)^2 + (4.8 - 3.787)^2 + (5.6 - 3.787)^2 + (5.2 - 3.787)^2 + (2.9 - 3.787)^2 + (3.7 - 3.787)^2 + (3 - 3.787)^2 + (3.6 - 3.787)^2 + (2.8 - 3.787)^2 + (4.8 - 3.787)^2)/15 = 0.8798

Standard deviation = sqrt(0.8798) = 0.938

B) At 95% confidence interval the critical value is z0.025 = +/- 1.96

The confidence interval is

Mean +/- z0.025 * SD/sqrt (n)

= 3.787 +/- 1.96 * 0.938/sqrt(15)

= 3.787 +/- 0.475

= 3.312, 4.262

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