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Alexandra [31]
3 years ago
6

Two processes in a manufacturing line are performed manually: operation A and operation B. A random sample of 50 different assem

blies using operation A shows that the sample average time per assembly is 8.05 minutes, with a population standard deviation of 1.36 minutes. A random sample of 38 different assemblies using operation B shows that the sample average time per assembly is 7.26 minutes, with a population standard deviation of 1.06 minutes.
Required:
For α = 0.10, is there enough evidence in these samples to declare that operation A takes significantly longer to perform than operation B?
Mathematics
1 answer:
MArishka [77]3 years ago
4 0

Answer:

3.06

Step-by-step explanation:

The correct answer is - 3.06

Reason -

For sample A :

mean, \bar{x_{1} } = 8.05          

Standard deviation, \sigma_{1} = 1.36          

Size, n_{1} = 50          

                 

For sample B :

mean, \bar{x_{2} } = 7.26          

Standard deviation, \sigma_{2} = 1.06          

Size, n_{2} = 38

Now,

\bar{x_{1} } - \bar{x_{2} }  = 8.05 - 7.26 = 0.79

Standard deviation error, SE = √(\sigma_{1}²/n_{1} + \sigma_{2}²/n_{2})  = 0.2580

Now,

Z-statistic = (\bar{x_{1} } - \bar{x_{2} } )/ SE

                = 0.79/0.2580

                = 3.06

⇒Z-statistic = 3.06

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