A is the mean first sample thickness B is the mean second

?_A - is the mean first sample thickness.

?_B - is the mean second sample thickness.

a) ?_A-?_B? ?

The thickness of a plastic film (in mils) on a substrate material is thought to be influenced by the temperature at which the coating is applied. A completely randomized experiment is carried out. 11 substrates are coated at 125?F, resulting in a sample mean coating thickness ofx Subscript 1 Baseline Overscript bar EndScripts = 102.28 and a sample standard deviation ofs1 = 5.08. Another 13 substrates are coated at 150?F, for which x Subscript 2 Baseline Overscript bar EndScripts = 104.70 ands2 = 20.15 are observed. It was originally suspected that raising the process temperature would reduce mean coating thickness. Do the data support this claim? Use a one-sided 99% CI to answer. Assume variances are unequal. ?A - is the mean first sample thickness. ?B - is the mean second sample thickness. a) ?A-?B? ?

Solution

We have two samples here and their findings are as follows:

n1 = 11, mua = 102.28 and sigma a = 5.08

n2 = 13, mub = 104.70 and sigmab = 20.15

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This is comparison of two sample means whose sample variances are known

H0: muA-muB = 102.28-104.70 = 0

Ha: muA-muB not equals 0

Two tailed hypothesis test.

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Observed difference (Sample 1 - Sample 2): -2.42
Standard Deviation of Difference : 5.7947

Unequal Variances
DF : 13
95% Confidence Interval for the Difference ( -14.9389 , 10.0989 )
T-Value -0.4176
Population 1 ? Population 2: P-Value = 0.683

N Mean StDev SE Mean Sample 1 11 102.28 5.08 1.5317 Sample 2 13 104.70 20.15 5.5886

2 Sample t Tutorial