A process that produces computer chips has a mean of .04 defective chips and a standard deviation of .003 chips. The allowable v
1 answer:
Answer:
The capability index for the process is 0.889
Step-by-step explanation:
Here, we want to compute the capability index for the process
To get this, we need some important parameters which we already have stated in the question
USL ( upper standard limit) = 0.048
LSL (lower standard limit) = 0.032
mean = 0.04
standard deviation = 0.003
We apply the formula as seen in the attachment below
Kindly understand that we are to calculate the Z upper and Z lower
The smallest value between the two will be our Z minimum
This is what we shall apply in the capability index formula which mathematically is;
Z minimum/3
From calculation:
Z lower = Z upper = 2.67
So therefore;
capability index = 2.67/3 = 0.889
You might be interested in
Answer:
Null hypothesis:
Alternative hypothesis:
A type of error II for this case would be FAIL to reject the null hypothesis that the population proportion is equal to 0.0147 when actually the alternative hypothesis is true (the true proportion is different from 0.0147).
Step-by-step explanation:
Previous concepts
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
Type I error, also known as a “false positive” is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.
Type II error, also known as a "false negative" is the error of not rejecting a null hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power.
Solution to the problem
On this case we want to test if the proportion of children diagnosed with Autism Spectrum Disorder (ASD) is different from 0.0147, so the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
A type of error II for this case would be FAIL to reject the null hypothesis that the population proportion is equal to 0.0147 when actually the alternative hypothesis is true (the true proportion is different from 0.0147).