Consider the following matched-pairs sample that represents observations before and after an experiment. Assume that the sample differences are normally distributed. Hint: The differences are calculated as Xafter - Xbefore.(You may find it useful to reference the appropriate table:z tableort table)

Before2.51.81.42.91.21.93.12.5After2.93.13.91.80.20.62.52.9

a.Construct the competing hypotheses to determine if the experiment increases the value of the observations.

• H₀:_D= 0;H_A:_D 0
• H₀:_D 0;H_A:_D< 0
• H₀:_D 0;H_A:_D> 0

b.Calculate the value of the test statistic.(Negative value should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

c.Find thep-value?

• p-value < 0.01
• 0.01 p-value < 0.025
• 0.025 p-value < 0.05
• 0.05 p-value < 0.10
• p-value 0.10

d.What is the conclusion to the hypothesis test?

e.Do the results change if we implement the test at a 1% significance level?

• Yes
• No