Often it is important in manufacturing to determine if an improved product, proc

ID: 3156117 • Letter: O

Question

Often it is important in manufacturing to determine if an improved product, process, or material is going to operate better than the ones currently used. The test for determining if there is really a benefit is the hypothesis test. If there are more than 30 in the sample then a standard z-test can be used. The test is used to check the treatment against chance. That is to mathematically show that there is a difference in the product, process, or material and that the difference is not because of chance. Your manufacturing facility is interested in determining if TiN coated HSS drill bits will cut more parts than standard non-coated HSS drill bits. The data below was gathered from production records within your facility. The data indicating number of parts per drill bit was randomly selected. Develop a hypothesis test and determine if the TiN coated drill bits cut more parts than the HSS drill bits. Non-coated HSS drill bit historical mean & sigma 18 parts per bit; standard deviation 2.1 Sample TiN drill bit data

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu = 18

H1 : mu > 18

Assume alpha = 5% = 0.05

sd = 2.1

Here we use z-test because population standard deviation is known and sample size is large.

This we can done using MINITAB.

Steps :

Enter data into MINITAB sheet --> Stat --> Basic statistics --> 1-Sample Z (Test and COnfidence Interval) --> Samples in columns --> select column where the data --> standard deviation : 2.1 --> Perform hypothesis test --> Hypothesize mean : 18 --> Options --> Confidence level : 95.0 --> Alternative : select greator than --> ok --> ok

Result is :

One-Sample Z: C1

Test of mu = 18 vs > 18
The assumed standard deviation = 2.1

95%
Lower
Variable N Mean StDev SE Mean Bound Z P
C1 84 18.4524 1.8262 0.2291 18.0755 1.97 0.024

Test statistic Z = 1.97

P-value = 0.024

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that the Tin coated drill bits cut more parts than the HSS drill bits.

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Often it is important in manufacturing to determine if an improved product, proc

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