Step 1 :Given values are: sample mean = 31.9, population mean = 30, standard deviation = 1.8, sample size = 17, and significance level = 0.10.
Step 2 :Calculate the z-score using the formula \((\text{sample mean} - \text{population mean}) / (\text{standard deviation} / \sqrt{\text{sample size}})\).
Step 3 :Substitute the given values into the formula to get the z-score: \(z = (31.9 - 30) / (1.8 / \sqrt{17}) = 4.352167049263083\).
Step 4 :The critical value for a two-tailed test at a significance level of 0.10 is 1.645.
Step 5 :Compare the z-score with the critical value. If the z-score is greater than the critical value, reject the null hypothesis and shut down the process. If the z-score is less than the critical value, fail to reject the null hypothesis and do not shut down the process.
Step 6 :Since the z-score (4.352167049263083) is greater than the critical value (1.645), the decision is to reject the null hypothesis and shut down the process.
Step 7 :Final Answer: \(\boxed{\text{Reject the null hypothesis and shut down the process}}\)