Using the steps in hypothesis testing, test the following hypotheses using the appropriate test statistic. Manually compute for them first and then use computer software and then compare your results.

1. A teacher would like to know if the class will be able to absorb the lecture from a guest speaker, so he made them take a pre-quiz before the lecture and a post-quiz after the lecture. The teacher would like to know if there is a significant difference between the pre-quiz scores and the post-quiz scores of the students (note that they are in a specific order):
2. Pre-quiz: 14,12,16,15,10,14,15
3. Post-quiz: 25,25,26,23,21,24,25

1. A student would like to know which establishment would allow him to save more money from everyday food costs. He is choosing between AVM or Hollywood Terraces, so he traced his spending in both establishments for 1 school week each, his data is as follows:
2. AVM: 97, 85, 69, 105, 105
3. HT: 60, 45, 60, 75, 100

Find out if there is a significant difference in his spending between the two food courts.

1. A sports researcher would like to determine if the "wonder wristband" can increase the speed of runners. He took the 100m dash time of 6 runners before wearing the bracelet, their time follows: 9.82, 10.12, 7.89, 8.12, 8.59, 8.49 and then the same runners' time while wearing the bracelet: 9.99, 10.52, 7.50, 6.54, 8.99, 6.87. Find out if there is a significant difference in time without the bracelet and with the bracelet