Question

In an effort to determine which of two manufacturing methods used by workers produces the greatest number of parts, the research department for ABC Manufacturing randomly selected six workers who make the same part and measured the six workers’ output using Method 1 and again using Method 2.   Test that the mean productivity between the two methods is the same at α=0.05. State the hypothesis in terms of Method 2 - Method 1.

Method 1	58	59	45	55	60	49
Method 2	52	49	47	44	53	50

For the 90% confidence interval for µ_Method2 - µ_Method1, find the upper endpoint.

Please explain how to get the answer, as it is very confusing to grasp the concept.

Thank you!

Answer 1

SOLUTION:

From given data,

Method 1

= / = (58+59+45+55+60+49)/6 = 326/6 = 54.333

= sqrt( (-)^2  /(-1))

= sqrt(((58-54.333)^2+(59-54.333)^2+(45-54.333)^2+(55-54.333)^2+(60-54.333)^2+(49-54.333)^2)/(6-1))

= 6.0553

Method 2

= / = (52+49+47+44+53+50)/6 = 295/6 = 49.167

= sqrt( (-)^2  /(-1))

= sqrt(((52-49.167)^2+(49-49.167)^2+(47-49.167)^2+(44-49.167)^2+(53-49.167)^2+(50-49.167)^2)/(6-1))

= 3.3116

For the 90% confidence interval for _Method2 - _Method1, find the upper endpoint.

90% = 90/100 = 0.90

= 1-0.90 = 0.1

/2 = 0.1/2= 0.05

Degree of freedom = df = +-2 =  6+6-2 = 10

Critical value:

t_/2,df = t_{0.05​​​​​​​,10} = 1.812

upper endpoint

(-) + t_/2,df* sqrt(/+/)

(54.333-49.167) +1.812* sqrt((6.0553)^2/6+(3.3116)^2/6​​​​​​​)

5.166 +1.812* 2.8176039

5.166 +5.1054982668

10.271498

upper endpoint = 10.2715