Question 4 25 Points Show ALL your workings; marks are allocated based on the details provided. Cherries Beauty Supplies (CBS) produces bottles of shampoo. When operating correctly, the company produces bottles whose contents weigh, on average, 25 ounces. A random sample of nine bottles from a single production run yielded the following content weights (in ounces): 21.4; 19.7: 19.7; 20.6; 20.8; 20.1; 19.7; 20.3; 20.9. Assuming that the population distribution is normal. Test at the 5% level against a two-sided alternative. 1) Formulate the null and alternative two-tailed hypotheses. (4 Marks) ii) Calculate the sample mean. (2 Marks) iii) Calculate the sample standard deviation. (6 Marks) iv) What are the critical values using a significance level of 5%? (4 Marks) v) Calculate the test statistic. (5 Marks) vi) Based on your answers to parts (iv) and (v) above, provide a response to CBS whether the manufacturing process is operating correctly. (4 Marks)