9.6 With coating C, the number of times a drill bit can be used before it must b
ID: 3154277 • Letter: 9
Question
9.6 With coating C, the number of times a drill bit can be used before it must be replaced has mean, = 237.5, and standard deviation, = 7.1. A new coating, N, is claimed to produce a higher mean and it is desired to test this claim statistically. Assume the standard deviation for the new coating is the same as for coating C.
(a) Define a parameter to be used in determining the hypotheses for this testing situation and state the null and alternative hypotheses in terms of this parameter.
(b) What are the practical consequences of a type I error in this situation?
(c) What are the practical consequences of a type II error in this situation?
(d) In a random sample of n=36 bits with the new coating, = 240.1. What conclusion is reached with = .05?
(e) What is the p-value for this testing situation?
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 237.5
Ha: u > 237.5 [ANSWER]
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b)
A type I error is when we conclude that the new coating has a higher mean number of times it can be used, when in fact, its mean is not higher.
Hence, you will buy a probably more expensive coating that is not really better in quality.
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c)
A type II error is when we conclude that the new coating doesn't have a higher mean number of times it can be used, when in fact, its mean is higher.
Hence, you will not buy a coating that is actually better in quality.
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d)
As we can see, this is a right tailed test.
Thus, getting the critical z, as alpha = 0.05 ,
alpha = 0.05
zcrit = + 1.644853627
Getting the test statistic, as
X = sample mean = 240.1
uo = hypothesized mean = 237.5
n = sample size = 36
s = standard deviation = 7.1
Thus, z = (X - uo) * sqrt(n) / s = 2.197183099
As z > 1.645, we REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence that the new coating has a higher mean number of times it can be used at 0.05 level. [ANSWER]
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e)
Also, the p value is, as this is one tailed,
p = 0.014003686 [ANSWER]
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