Question

Four brands of lightbulbs are being considered for use in the final assembly area of the Ford F-150 truck plant in Dearborn, Michigan. The director of purchasing asked for samples of 200 from each manufacturer. The numbers of acceptable and unacceptable bulbs from each manufacturer are shown below. At the 0.05 significance level, is there a difference in the quality of the bulbs?

	Manufacturer
	A				B				C				D
Unacceptable		32				14				9				23
Acceptable		168				186				191				177
Total		200				200				200				200

H₀: There is no relationship between quality and manufacturer.

H₁: There is a relationship.

State the decision rule using 0.05 significance level. (Round your answer to 3 decimal places.)

Reject H0 if chi-square > _____.

Compute the value of chi-square. (Round your answer to 3 decimal places.)

Chi-square value: _____

What is your decision regarding H₀?

Reject or Do not reject H0. There is Sufficient or Insufficient evidence to conclude that a relationship exists between quality and manufacturer.

Answer 1

Step 1:

Ho: There is no relationship between quality and manufacturer, both variables are independent

H1: There is a relationship, both variables are not independent.

Step 2: Decision rule

Level of significance = 0.05

df = (2-1)* (4-1) = 3

Chi square critical = CHISQ.INV.RT(probability,df) = CHISQ.INV.RT(0.05 , 3) = 7.815

Rejection rule : ( , > 7.815)

Step 3: Test statistics

data	A	B	C	D	total
Unacceptable	32	14	9	23	78
Acceptatble	168	186	191	177	722
total	200	200	200	200	800

Expected values

Expected value	A	B	C	D	total
Unacceptable	20	20	20	20	78
Acceptatble	181	181	181	181	722
Total	200	200	200	200	800

Squared distance

squared distance	A	B	C	D	total
Unacceptable	8.013	1.551	5.654	0.628	15.846
Acceptatble	0.866	0.168	0.611	0.068	1.712
Total	8.878	1.719	6.265	0.696	17.558

= 17.558

As the (17.558) is greater than critical (7.815), we reject the Nul hypothesis.

Hence there is sufficient evidene to conclude that a relashionship exists between quality and manufacturer.