Question

A manager at a furniture production plant created an incentive plan for her carpenters in order to decrease the number of defects in the furniture production. She wants to check if the incentive plan worked. The manager selected 11 carpenters at random, recorded their annual defects before and after the incentive and came up with the following:

Salesperson	Before	After
Sanjeev Shippy	38	16
Cody Finney	20	32
Becky Braddy	27	16
Calvin Morrill	33	20
Becky Gilbert	33	21
Agnessa Becker	27	19
Wynn Satterlee	35	16
Karina Presley	26	27
Dalya Becker	24	24
Stefan Finney	33	15
Calvin Gilbert	29	24

Notice, that a positive outcome of an incentive plan is confirmed with a positive mean of the differences (difference equals before minus after).

Given that the null hypothesis and the alternative hypothesis are:

  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 in favour of H1 if the computed value of the statistic is less than 1.372.
	Reject H0 in favour of H1 if the computed value of the statistic is between -1.372 and 1.372.
	Reject H0 in favour of H1 if the computed value of the statistic is greater than 1.81.
	Reject H0 in favour of H1 if the computed value of the statistic is between -1.81 and 1.81.
	Reject H0 in favour of H1 if the computed value of the statistic is greater than 1.372.
	None of the above.

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

Mean: 0

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

Test statistic: 0

d)

What is your decision regarding H₀?

	There is sufficient evidence, at the given significance level, to reject H0 and accept H1.
	There is insufficient evidence, at the given significance level, to reject H0 and so H0 will be accepted or at least not rejected
	There is insufficient evidence to make it clear as to whether we should reject or not reject the null hypothesis

Answer 1

Given that the null hypothesis and the alternative hypothesis are:

  H₀: μ_d ≤ 0
  H₁: μ_d > 0 (Right tailed test)

Critical Value of t with degrees of freedom= 10 is 1.372.

a) State the decision rule:

Reject H0 in favour of H1 if the computed value of the statistic is greater than 1.372.

b) Mean of difference = 8.64

c) Test statistic= dbar/sd/sqrt(n)= 8.64/10.08/sqrt(11)

t= 2.84

d) decision regarding H_{0 There is sufficient evidence, at the given significance level, to reject H0 and accept H1.}