Essay about Quality Associates Case

578 Words Dec 12th, 2010 3 Pages
1) Conduct a hypothesis Test for each sample at the .01 level of significance and determine what action if any should be taken. Provide the test-statistic and p-value for each test.
Sample 1 1) H0: μ = 12
Ha: μ ≠ 12 2) α = .01, but for two-tail test will = .005 3) Z = (x-bar – μ) / (σ/√n) 4) Z Critical value at .005 = 2.575 5) Z = (11.9587 – 12) / (.21/√30) = -1.077187
The observed value lies outside the rejection region, so we fail to reject H0. 6) P –value is between .2814 for a two-tailed test
Sample 2 1) H0: μ = 12
Ha: μ ≠ 12 2) α = .01, but for two-tail test will = .005 3) Z = (x-bar – μ) / (σ/√n) 4) Z Critical value at .005 = 2.575 5) Z = (12.0287 – 12) / (.21/√30) = .74855
The
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Based on our 4 samples, the standard deviation for the population appears to be slightly lower than .21, but not much. 3) Compute limits for the sample mean x-bar around mu=12 such that, as long as new sample mean is within those limits, the process will be deemed to be operating satisfactorily. If x-bar exceeds the upper limit or is below the lower limit, corrective action will be taken. These limits are referred to as upper and lower control limits for quality control purposes.
Upper Limit: μ + 3 σx-- = 12 + 3(.21/√30) = 12.115
Lower Limit: μ - 3 σx-- = 12 – 3(.21/√30) = 11.885
This shows that sample 3 is very close to falling below the lower limit and would need corrective action, but at the current time all 4 samples are within this range for performing satisfactorily. 4) Discuss the implications of changing the level of significance to a larger value. What mistake or error could increase if the level of significance is increased?
The larger the level of significance, the smaller our interval will be. This will result in more Type 1 Errors as more null hypotheses are rejected since we have a narrower critical region and a wider rejection region with an increased
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