The corrosive effects of various soils on coated and uncoated steel pipe was tes

Question

The corrosive effects of various soils on coated and uncoated steel pipe was tested by using a dependent sampling plan. The data collected are summarized below, where d is the amount of corrosion on the coated portion subtracted from the amount of corrosion on the uncoated portion. Does this random sample provide sufficient reason to conclude that the coating is beneficial? Use = 0.01 and assume normality.

n = 40, d = 222, d2 = 6133

(a) Find t. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer correct to four decimal places.)

Explanation / Answer

Given

N=40

sigma(d)=222

sigma(d2)=variance=6133

standard deviation

=sqrt(variance)= 78.313

standard error

=standard deviation/sqrt(n)

=78.313/sqrt(40)

=12.38

t-value

mean/standard error

=222/12.38

=17.9

for 0.01 significance level ,df =19 ,

p-value is approximately tends to 0 (very small value)

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