Question

A support used in an automotive application is supposed to have a nominal internal diameter of 1.5 inches. A random sample of 25 brackets is selected and the nominal internal diameter of these brackets is 1.4975 inches. The diameters of the supports are known to be normally distributed with a standard deviation of σ = 0.01 inches.

a) Perform the hypothesis test Ho: μ = 1.5 versus H1 ≠ 1.5 at an α = 0.01 using the 5 hypothesis test steps: 1. Establish the hypotheses

Ho:

H1:

2. Establish the test statistic

3. Establish the rejection zone Rejection Zone:

Graph showing rejection zone (Place the value on the vertical line where the rejection zone begins):

4. Calculate test statistics

5. Establish the conclusion Graph showing rejection zone and placement of test statistics. (Place the value on the vertical line that corresponds to the test statistic):

Based on the previous graph, establish the conclusion that applies to the problem.

b) Determine the p-value (probability of the test statistic) The p-value depends on whether the test is one-tailed or two-tailed. If the hypothesis test is of a tail, then the p-value is the value that comes directly from the probability of the test statistic. If the test is two-tailed, then the p-value is 2 times the probability obtained from looking for the probability of the test statistic

. The value of Ф (1.25) =

The value of α / 2 =

P-value =

c) Based on the p-value and considering an α = 0.01, what would be the decision? Reject or not reject Ho? Use the space to answer.

d) Use the following OC graph to approximate the probability of Type II Error for a true average diameter of 1,495. Start by calculating the value of parameter d with the following formula.

? = ⌈μ − μ0⌉? =

The value of Type II Error is approximately: β =            approximately

The "Power" of the test is: Power = 1 - β = approximately

e) What sample size is required to detect a true average diameter as low as 1,495 inches if we want the “Power” of the test to be 90%? Start by determining how much Error Type II of the “Power” = 1 - β ratio is.

β =

? =

⌈μ − μ0⌉? = n ≈

Answer 1

ANSWERED

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