Two formulations for a certain coating, designed to inhibit corrosion, are being

Question

Two formulations for a certain coating, designed to inhibit corrosion, are being tested. For each of eight pipes, half the pipe is coated with formulation A, and the other half is coated with formulation B. Each pipe is exposed to a wilt environment for 500 hours. Afterward, the corrosion loss (in mu m) is measured for each formulation on each pipe. Can you conclude that the mean amount of corrosion differs between the two formulations?, including null and alternative hypothesis. Write your conclusion in a complete sentence using nontechnical terms. Use alpha = 0.05.

Explanation / Answer

Null Hypothesis H0: Mean amount of corrosion in pipe A and pipe B is same.
Alternative Hypothesis H1: Mean amount of corrosion in pipe A and pipe B is different.

Mean amount of corrosion of pipe A (197,161,144,162,185,154,136,130) is 158.625
Mean amount of corrosion of pipe B (204,182,140,178,183,163,156,143) is 168.625

Std deviation of amount of corrosion of pipe A (197,161,144,162,185,154,136,130) is 23.15
Std deviation of amount of corrosion of pipe B (204,182,140,178,183,163,156,143) is 22.01

We will use the  two-sample t-test to determine whether the difference between means found in the sample is significantly different from the hypothesized difference between means.

Standard error, SE = sqrt[ (s12/n1) + (s22/n2) ]

SE = sqrt[ (23.152/8) + (22.012/8) ] = 11.29

Degree of freedom, DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }

DF = (23.152/8 + 22.012/8)2 / { [ (23.152 / 8)2 / (8 - 1) ] + [ (22.012 / 8)2 / (8 - 1) ] } = 14 (rounded to nearest integer)

t - stat = (Observed Difference - Hypothesized difference)/ SE

= (168.625 - 158.625)/11.29 = 0.8857

This is two-tail test, so the significance level = 0.05/2 = 0.025

p-value for t = 0.8857 and df=14 is 0.1953

As the p-value is greater than 0.025, we fail to reject the null hypothesis and conclude that there is not significant statistical evidence to show that mean amount of corrosion in pipe A and pipe B is different

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