Bottles of a popular cola are supposed to contain 300 militiers of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. From experience, the distribution of the contents is approximately Normal. An inspector measures the contents of six randomly selected bottles from a single day's production. The results are 299.4, 297.7, 301.0, 298.9, 300.2, 297.0
A) Do these data provide convincing evidence that the mean amount of cola in all bottles filled that day differs from the target value of 300 ml? Carry out an appropriate test to support your answer and SHOW ALL OF YOUR WORK.
B) Construct and interpret a 95% confidence interval for the population mean u. What additional information does the confidence interval provide?