Problem 3: A manufacturer fills soda bottles. Periodically the company tests to see if there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola. A random sample of 14 bottles of regular cola has a mean of 501.6 ml of soda with a standard deviation of 3.9 ml. A random sample of 16 bottles of diet cola has a mean of 498.9 ml of soda with a standard deviation of 5.3 ml. Test the claim that there is a difference between the mean fill levels for the two types of soda using a 0.01 level of significance. Assume that the population variances are not equal since different machines are used to fill bottles of regular cola and diet cola. All populations are approximately normal.

Fig: 1