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 α = 0.01 and assume normality. n = 48, Σd = 234, Σd2 = 6157

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

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

Answer 1

Here we have to perform paired t test because corrosive effect of various soils on coated and uncoated steel pipe was tested by dependent sampling plan.

So null hypothesis H_{​​​​​​0}: $\mu$_d = 0

Alternative hypothesis H​​​​​​1 : $\mu$_d$\neq$ 0

Given level of significance  $\alpha$ = 0.01