A manager at a furniture production plant created an incentiveplan for her carpenters in order to decrease the number of defectsin the furniture production. She wants to check if the incentiveplan worked. The manager selected 9 carpenters at random, recordedtheir annual defects before and after the incentive and came upwith the following:

Salesperson Before After Adrian Gilbert 29 17 Nikki Edwards 33 23 Abigail Gage 38 19 Marc Phillips 25 15 Orla Dille 26 32 Mary Bennett 38 18 Agnessa Presley 32 35 Radu Shippy 39 24 Josh Presley 35 24

Notice, that a positive outcome of an incentive plan isconfirmed with a positive mean of the differences (differenceequals before minus after).

Given that the null hypothesis and the alternative hypothesisare:

  H₀: μ_d ≤ 0
  H₁: μ_d > 0

and using a 0.1 significance level, answer the following:

a)

State the decision rule. Reject H0 infavour of H1 if the computed value of thestatistic is between -1.86 and 1.86. Reject H0 infavour of H1 if the computed value of thestatistic is greater than 1.397. Reject H0 infavour of H1 if the computed value of thestatistic is less than 1.397. Reject H0 infavour of H1 if the computed value of thestatistic is between -1.397 and 1.397. Reject H0 infavour of H1 if the computed value of thestatistic is greater than 1.86. None of the above.

b) Compute the mean of the difference.
For full marks your answer should be accurate to at least twodecimal places.

Mean: 0

c) What is the value of the test statistic?
For full marks your answer should be accurate to at least twodecimal places.

Test statistic: 0

d)

What is your decision regarding H0? There is sufficient evidence, atthe given significance level, to reject H0 andaccept H1. There is insufficient evidence, atthe given significance level, to reject H0 andso H0 will be accepted or at least notrejected There is insufficient evidence tomake it clear as to whether we should reject or not reject the nullhypothesis