4. In an attempt to compare the starting salaries of college graduates majoring in education and social sciences, random samples of 50 recent college graduates in each major were selected and the following information was obtained: Major Mean Standard deviation Education 3380 185 Social Science 3195 198 (a) Obtain the 90% confidence interval for the mean difference of starting salaries between education and social science major. (5 marks) (b) Do you think that the difference for the two groups is significant? Justify your answer. (2 marks)5. The manufacturer of a gasoline additive claims that the use of this additive increases gasoline mileage. A random sample of six cars was selected, and these cars were driven for I week without the gasoline additive and then for 1 week with the gasoline additive. The following table gives the miles per gallon for these cars without and with the gasoline additive. Without 24.6 28.3 18.9 23.7 15.4 29.5 with 26.3 31.7 18.2 25.3 18.3 30.9 (a) Construct a 99% confidence interval for the mean pa of the population of paired differences. (5 marks) (b) From the confidence interval constructed in (a), can you conclude that the usage of gasoline additive increase the gasoline mileage? Explain. (2 marks)