Case 1 Quality Associates, Inc. 1. Conduct a hypothesis test for each sample at

Question

Case 1 Quality Associates, Inc.

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.
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 around 12 such that, as long as a new
sample mean is within those limits, the process will be considered to be operating satisfactorily. If exceeds the upper limit or if 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.

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?

Sample 1 Sample 2 Sample 3 Sample 4 11.55 12.39 12.05 11.90 11.62 12.00 11.64 12.22 11.52 11.92 12.39 11.88 11.75 11.83 11.65 12.03 11.90 12.23 12.11 12.35 11.64 11.84 11.90 12.09 11.80 12.07 12.22 11.77 12.03 12.11 11.88 12.20 11.94 12.05 12.03 11.79 11.92 12.37 12.35 12.30 12.13 12.25 12.09 12.27 12.09 12.04 11.77 12.29 11.93 12.24 12.20 12.47 12.21 11.92 11.79 12.03 12.32 12.37 12.30 12.17 11.93 12.22 12.27 11.94 11.85 11.61 12.29 12.16 11.76 12.21 12.47 11.77 12.16 11.56 12.03 12.00 11.77 11.95 12.17 12.04 12.00 12.01 11.94 11.98 12.04 12.06 11.97 12.30 11.98 11.76 12.23 12.18 12.30 11.82 12.25 11.97 12.18 12.12 11.90 12.17 11.97 11.60 12.22 11.85 12.17 11.95 11.88 12.30 11.85 11.96 12.03 12.15 12.30 12.22 12.35 11.96 12.15 11.75 12.09 11.95

Explanation / Answer

Sample 1 30
Sample Mean 11.958667
Population Standard Deviation 0.220356

Hypothesized Value 12

Standard Error 0.04
Test Statistic Z -1.03

P-Value (Lower Tail) 0.1521
P- Value (Upper Tail) 0.8479
P-Value (Two Tail) 0.3042

We should not reject the null hypothesis and
no corrective action is needed.
Sample 2 30
Sample Mean 12.028667
Population Standard Deviation 0.220356

Hypothesized Value 12

Standard Error 0.04
Test Statistic Z 0.71

P-Value (Lower Tail) 0.7619
P- Value (Upper Tail) 0.2381
P-Value (Two Tail) 0.4761

We should not reject the null hypothesis and
no corrective action is needed.
Sample 3 30
Sample Mean 11.889
Population Standard Deviation 0.207171

Hypothesized Value 12

Standard Error 0.04
Test Statistic Z -12.93

P-Value (Lower Tail) 0.0017
P- Value (Upper Tail) 0.9983
P-Value (Two Tail) 0.0033

We should reject the null hypothesis and
corrective action is needed.
Sample 4 30
Sample Mean 12.081333
Population Standard Deviation 0.206109

Hypothesized Value 12

Standard Error 0.04
Test Statistic Z 2.16

P-Value (Lower Tail) 0.9847
P- Value (Upper Tail) 0.0153
P-Value (Two Tail) 0.0307

We should not reject the null hypothesis and
no corrective action is needed.

4.Based on the four samples, the standard deviation for each was close to .21. Two samples were above and two samples were below, so .21 is reasonable.
Lower Limit = 11.9012

Upper Limit = 12.0988
By using a higher value for the significance to a larger value, we are making the confidence interval smaller.

This increases our chances of making a type one error.
In summary, only sample three showed that corrective action was needed. This was found by comparing the p-value to the upper tail area at the 99% confidence level and further supported by the confidence interval that was found.

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