This is Introduction to probability and statistics.

Please answer all three parts clearly showing all the steps. (Please do not use excel, minitab, ...)

5. A tutor guarantees to his customers that his studying / learning tips will significantly improve their test scores . Exam scores ( before and after ) for five customers are provided below . 1 2 3 4 5 Before 50 47.5 52.5 49. 0 53.0 After 51 48. 0 52.5 49.5 53. 3 52 . State the appropriate null and alternative hypotheses to test whether the tutoring significantly improves test scores . ( 1 point ) 56 . Calculate the value of the test statistic . ( 3 points ) 5 c . Based on an alpha of 0. 05, determine whether you reject or fail to reject the null hypothesis . Justify your answer . ( 2 points )