Matched or Paired Samples · Exercise 2

A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in. The “before” value is matched to an “after” value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level.
$$\begin{array}{ccccccccc}\text{Installation}& \text{A}& \text{B}& \text{C}& \text{D}& \text{E}& \text{F}& \text{G}& \text{H}\\ \text{Before}& \text{3}& \text{6}& \text{4}& \text{2}& \text{5}& \text{8}& \text{2}& \text{6}\\ \text{After}& \text{1}& \text{5}& \text{2}& \text{0}& \text{1}& \text{0}& \text{2}& \text{2}\end{array}$$

State the null and alternative hypotheses.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §10.4 Matched or Paired Samples · Exercise 2