11. please show all work for this problem and round as far as possible thank you A...

11. please show all work for this problem and round as far as possible

thank you

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A pharmaceutical manufacturer is concerned about the impurity concentration in pills, and it is anxious that this concentration not exceed 3%. It is known that in any production run the impurity concentrations follow a normal distribution. A random sample of 25 pills from a production run was checked and the sample mean impurity concentration was found to be 3.35%. The sample standard deviation was 0.5. Test the null hypothesis that the population mean impurity concentration is 3% against the alternative that it is more than 3%. Use a 5% significance level. Answer the following, and round off your answer to three decimal places. (a) What is the test statistic used in the decision rule? (b) What is the critical value? (c) Can the null hypothesis be rejected at a 5% significance level? O A. Reject the null hypothesis. B. Do not reject the null hypothesis. A pharmaceutical manufacturer is concerned about the impurity concentration in pills, and it is anxious that this concentration not exceed 3%. It is known that in any production run the impurity concentrations follow a normal distribution. A random sample of 25 pills from a production run was checked and the sample mean impurity concentration was found to be 3.35%. The sample standard deviation was 0.5. Test the null hypothesis that the population mean impurity concentration is 3% against the alternative that it is more than 3%. Use a 5% significance level. Answer the following, and round off your answer to three decimal places. (a) What is the test statistic used in the decision rule? (b) What is the critical value? (c) Can the null hypothesis be rejected at a 5% significance level? O A. Reject the null hypothesis. B. Do not reject the null hypothesis.