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 9 carpenters at random, recorded their annual defects before and after the incentive and came up with 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 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 between -1.86 and 1.86. Reject H0 in favour of H1 if the computed value of the statistic is greater than 1.397. Reject H0 in favour of H1 if the computed value of the statistic is less than 1.397. Reject H0 in favour of H1 if the computed value of the statistic is between -1.397 and 1.397. Reject H0 in favour of H1 if the computed value of the statistic 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 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

Let :

x:- Carpenters annual defects before the incentive

y:- carpenters annual defects before after the incentive

d = difference between the annual defects before & after the incentive

d= x-y

Let μd = population mean the difference between the annual defects before & after the incentive.

We want to find that the incentive decreases the annual defects

Given that the null hypothesis and the alternative hypothesis are:

  H0: μd ≤ 0
  H1: μd > 0

a) n = 9. df= n-1 = 9-1 = 8

at the 0.1 significance level, alpha = 0.10

the critical value is tdf,alpha = t 8,0.1  = 1.397.....from t table

Decision rule is Reject Ho if test statistic > 1.397

Answer:- Reject H0 in favour of H1 if the computed value of the statistic is greater than 1.397.

b)

x	y	d=x-y	d^2
29	17	12	144
33	23	10	100
38	19	19	361
25	15	10	100
26	32	-6	36
38	18	20	400
32	35	-3	9
39	24	15	225
35	24	11	121
Total		88	1496