Question

Recently, the RMC manufacturing facility in Tupelo, Mississippi has been experiencing problems with one of their suppliers. This supplier provides a part for which the key quality characteristic is its weight. The problem has not been with the average weight. Instead, parts received at the Tupelo facility have been exhibiting excessive weight variability. Under normal conditions, the standard deviation in weight should be less than or equal to 4 g. To deal with this problem, a RMC quality engineer has decided to implement a test of hypotheses on each shipment of parts received at the facility. This test is to have a level of significance of 0.05 and can be summarized as follows where o denotes the standard deviation of part weight Ho: o 3 4g H: 0 > 4g In designing this test, the engineer wishes to have a Type II error probability of 0.1 when the true standard deviation rises to 10 g. Part a (5 points): State any assumptions that are required to perform this test. Part b (5 points): Determine the appropriate sample size for this test. You may use this sample size for the remainder of the problem. Part c (4 points): What is the power of this test if the true standard deviation of part weight is o = 12 g? Suppose a shipment is received, a random sample of parts is measured, and the resulting sample standard deviation is 5.5 g. Part d (6 points): Identify the test statistic and critical region for the test. State the conclusion for this test. Part e (5 points): Construct an appropriate confidence interval to verify your conclusion from part d. Part f (5 points): What is the P-value for this test? State the conclusion for this test. (An interval of probabilities is enough for the P-value)

Answer 1

Part a)

Now and again theory tests on the populace change or standard deviation are required. At the point when the populace is displayed by a typical circulation, the tests and spans portrayed beneath are material. While tests on implies are moderately inhumane toward the typicality suspicion, the test system for change is definitely not.

Part b)

Assume that we wish to test the speculation that the change of an ordinary populace $\sigma$ 2 equivalents a predefined esteem $\sigma$ 02, state or proportionately, that the standard deviation is $\sigma$ equivalent to $\sigma$ 0.

the guessed estimation of the standard deviation is not exactly or equivalent to 4g. Assume that if the genuine standard deviation ascends to 12g. Type II blunder likelihood is equivalent to 0.1.

$\lambda$ = 12g/4g =3.

level of criticalness = 0.05

From the working trademark bend with $\beta$ = 0.20 and $\lambda$ = 0.1, we find that example size (n) = 15,

c)

The intensity of a factual test is the likelihood of dismissing the invalid speculation H0 when the elective theory is valid. The intensity of a measurable test = 1 -$\beta$ =0.8.