Managerial Report 1 Conduct a hypothesis test for each sampl

Managerial Report:

1) Conduct a hypothesis test for each sample at the .01 level of significance and determine what action, if any, should be take. Provide the test statistic and p-value for each test.

2) Compute the standard deviation for each of the four samples. Does the assumption of .21 for the population standard deviation appear reasonable?

3) Compute limits for the sample mean X around =12 such that, as long as a new sample mean is within those limits, the process will be considered to be operating satifactorily. If X exceeds the upper limit or if X is below the lower limit, corrective action will be taken. These limits are refferred to as upper and lower control limits fro quality control purposes.

4) Discuss the implications of changing the level of significance to a larger value. What mistakes or error could increase if the level of significance in increased?

Solution

ample 1
1) H0: = 12
Ha: 12
2) = .01, but for two-tail test will = .005
3) Z = (x-bar – ) / (/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: = 12
Ha: 12
2) = .01, but for two-tail test will = .005
3) Z = (x-bar – ) / (/n)
4) Z Critical value at .005 = 2.575
5) Z = (12.0287 – 12) / (.21/30) = .74855
The observed value lies outside the rejection region, so we fail to reject H0.
6) P-value is 0.4541 for a two-tailed test
Sample 3
1) H0: = 12
Ha: 12
2) = .01, but for two-tail test will = .005
3) Z = (x-bar – ) / (/n)
4) Z Critical value at .005 = 2.575
5) Z = (11.889 – 12) / (.21/30) = - 2.895
The observed value lies inside the rejection region, so we reject H0.
6) P-Value is .0038 for a two-tailed test

Sample 4
1) H0: = 12
Ha: 12
2) = .01, but for two-tail test will = .005
3) Z = (x-bar – ) / (/n)
4) Z Critical value at .005 = 2.575
5) Z = (12.081 – 12) / (.21/30) = 2.11264
The observed value lies outside the rejection region, so we fail to reject H0.
6) P-value is .034 for a two-tailed test

Sample 1 Standard Deviation = 0.22035603
Sample 2 Standard Deviation = 0.22035603
Sample 3 Standard Deviation = 0.207170594
Sample 4 Standard Deviation = 0.206108999
Yes it appears reasonable since our 4 samples have standard deviations just above .21 in 2 cases and just below .21 in 2 cases.