In this case, we have Quality Associates, Inc. a consulting firm advising its client about sampling and statistical procedures that can be used to control their manufacturing process. Their client has offered samples to be analyzed, so they can quickly learn whether the process is operating satisfactorily or corrective actions needs to be taken. The numbers given in the case were as follows: assumed population standard deviation is equal to .21, sample size is equal to 30 and the test value of the mean was 12. They also stated the two hypotheses to be tested: the null hypothesis that the population is equal to 12 and the alternative hypothesis that the mean is not equal to 12. This indicates a two tailed tests to determine whether or not to reject the null hypothesis. The 4 provided sample sizes each contained 30 observations, indicating a normal distribution and z test statistics.
The first question required conducting a hypothesis test for each sample at the .01 level of significance. Based upon the test, determine if any corrective actions need to be taken. There are two approaches to hypothesis testing, the p-value approach and the critical value approach. The first step for the p-value approach was to calculate the mean for each sample. In order, they were: 11.9587| 12.0287| 11.8890| 12.0813|
Next, was to calculate standard error, by using the formula sigma divided by the square root of n. This came out to be .0383. To find the z test statistic subtract the test value of 12 from the sample mean and divide by the standard error.
The z test statistic for each sample were as follows:
-1.0966| 0.7493| -2.8982| 2.1227|
The 1 tail p-value could then be found by using the normsdist function in Excel. This function indicates probability to the left of the value, so positive numbers were subtracted from 1. Since this is a two tailed test, the values were...