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# Quality Associates Inc.

Quality Associates Inc., a consultancy company aims to offer sampling and statistical information to a customer. The mean 12 and the standard 0.21 variance for a sample of the satisfactory client method are calculated. Successive samples of 30 findings are collected at random to assess the customers' satisfaction level. The method of the client was deemed successful if the average was 12. If the mean was substantially different for this process from 12, then the process would be unsatisfactory and corrective steps needed to restore it to the level of organizational satisfaction. The following table shows the descriptive statistics for the four successive samples obtained for the process.SUMMARYGroupsCountSumAverageVarianceStandard deviationSample 130358.7611.958670.0485570.220356Sample 230360.8612.028670.0485570.220356Sample 330356.6711.8890.042920.207171Sample 430362.4412.081330.0424810.206109The process mean for sample 1 is 11.96, sample 2 is 12.03, sample 3 is 11.89 and sample 4 is 12.08. The standard deviation for sample 1 and sample 2 is 0.22 while the standard deviation for sample 3 and sample 4 is 0.21. The study assumes that the four standard deviations are equal. The assumption of the equality of variances appears reasonable because the standard deviations for sample 3 and 4 are equal to the population standard deviation while the standard deviation for sample 1 and 2 have a small difference from the population standard deviation.MethodThe study will use inferential statistics to evaluate the satisfaction of the client’s process. Sample t-tests will be used to determine the significance of the difference between the population mean and the sample mean. Microsoft Excel software will be used to analyze the data.ResultsThe significance of the difference between the each sample mean and the population mean will be determined. The table below shows the results of the independent sample t-test for the difference between mean for sample 1 and population mean.One-Sample TestTest Value = 12tdfSig. (2-tailed)Mean Difference99% Confidence Interval of the DifferenceLowerUpperSample 1-1.02729.313-.04133-.1522.0696The process mean for sample 1 is significantly equal to the population mean, 12. This is because the p-value, 0.313 is greater than the level of significance, 1%. Therefore, the null hypothesis is not rejected.The table below shows the t-test results for sample 2.One-Sample TestTest Value = 12tdfSig. (2-tailed)Mean Difference99% Confidence Interval of the DifferenceLowerUpperSample 2.71329.482.02867-.0822.1396The p-value, 0.482 is greater than the level of significance, 1%. The test statistic is not significant. Therefore, the null hypothesis is not rejected. The process mean for sample 2 is significantly equal to the population mean.The table below shows the result for sample t-test on sample 3One-Sample TestTest Value = 12tdfSig. (2-tailed)Mean Difference99% Confidence Interval of the DifferenceLowerUpperSample 3-2.93529.006-.11100-.2153-.0067The test statistic is significant because the p-value, 0.006 is lower than the level of significance, 1%. Therefore, the null hypothesis is rejected. The process mean for sample 3 is different from the population mean.The table below shows the t-test results for the mean of process 4.One-Sample TestTest Value = 12tdfSig. (2-tailed)Mean Difference99% Confidence Interval of the DifferenceLowerUpperSample 42.16129.039.08133-.0224.1851The test statistic is insignificant because the p-value, 0.039 is greater than the level of significance, 1%. Therefore, the null hypothesis is not rejected. The mean process mean for sample 4 is significantly equal to the population process mean.Further, we wish to determine whether there exists significant differences among the sample process means for the four samples. The table below shows the results of the analysis of variance (ANOVA) to determine the significance of the difference among the groups.ANOVAValueSum of SquaresdfMean SquareFSig.Between Groups.6313.2104.606.004Within Groups5.293116.046Total5.923119The test statistic, F = 4.606 is significant because the p-value, 0.004 is less than the level of significance, 1%. Therefore, the null hypothesis is rejected. We, therefore, conclude that at least one of the sample means is significantly different from the others. The table below shows the comparison between the sample means.ValueTukey BSampleNSubset for alpha = 0.0512Sample 33011.8890Sample 13011.958711.9587Sample 23012.0287Sample 43012.0813Means for groups in homogeneous subsets are displayed.a. Uses Harmonic Mean Sample Size = 30.000.The sample mean for sample 3 and sample 1 are equal. Sample means for sample 1, sample 2 and sample 4 are also significantly equal. However, the sample mean for sample 3 is significantly different from the sample mean for sample 2 and sample 4.The table below shows the confidence intervals for the sample means.Sample 1 Sample 2 Sample 3 Sample 4 Confidence Level(99.0%)0.11089Confidence Level(99.0%)0.11089Confidence Level(99.0%)0.10426Confidence Level(99.0%)0.10372Lower limit11.8478Lower limit11.9178Lower limit11.7847Lower limit11.9776Upper limit12.0696Upper limit12.1396Upper limit11.9933Upper limit12.1851The confidence intervals for sample 1, sample 2 and sample 4 are inclusive of 12. This implies that the sample means are significantly equal to 12. However, the confidence interval for sample 3 is different from 12.ConclusionThe sample t-test shows that all the sample means are equal to 12 except the mean for sample 3. Therefore, there is a need for corrective action after the time when sample 3 was obtained. The corrective actions would be necessary to increase mean of the process to 12 since the sample mean was less than 12.The results of the test could be affected by choice of the significance level. When the significance level is increased, the acceptance region for the study is reduced (Robert, 2013). This in effect reduces the probability of rejecting the null hypothesis. Thus, the increase in the significance level increases the probability of type I error and reduces the probability of type II error (Murray & Larry, 2014)ReferencesMurray, S. R., & Larry, S. J. (2014). Statistics. New York: McGraw-Hill.Robert, D. J. (2013). Business statistics. Boston: Pearson..