Answer: To answer this question, we need to perform a hypothesis test. The null hypothesis is that the standard deviation of the process is 2 mg or less, and the alternative hypothesis is that the standard deviation of the process is over 2 mg.
To test this hypothesis, we need to calculate the test statistic, which is the z-score. The z-score tells us how many standard deviations a given data point is from the mean. In this case, the z-score is calculated by subtracting the mean of the sample from the hypothesized mean of the population, and dividing that difference by the standard deviation of the sample:
z = (20.2 - 20) / 2.4 = 0.1
Since the z-score is positive, we know that the mean of the sample is greater than the hypothesized mean of the population. However, we need to compare this z-score to the critical value to determine whether it is statistically significant.
The critical value is the z-score that marks the cutoff between the region of acceptance and the region of rejection of the null hypothesis. For a 1% level of significance, the critical value is the z-score that marks the 99th percentile of the normal distribution. Since the normal distribution is symmetrical, this means that the critical value is 2.58 standard deviations from the mean.
Since the z-score we calculated is less than the critical value, we cannot reject the null hypothesis. This means that we cannot assert that the standard deviation of the process is over 2 mg at a 1% level of significance.