I am practicing Two-Sample Hypothesis Testing. Please help me to understand how I would write the null and alternative hypotheses for these questions. Also which test would you use and why. Here are the options:

1. t-Test: Paired Two Sample for Means
2. t-Test: Two-Sample Assuming Equal Variances
3. t-Test: Two-Sample Assuming Unequal Variances
4. z-Test: Two-Sample for Means

1. At the beginning and end of a four-week exercise program, the weights of nine adults were taken. Use the data below to test the claim that the program helps students to lose weight.

Start Weight (lbs)	118	126	134	162	145	188	173	125	137
End Weight (lbs)	123	131	132	159	138	182	170	128	137

2. is believed that freshmen at MU earn higher averages in Stats than do the sophomores. The results of past classes reveal an average for the freshmen (n=57) of 83.63 with a standard deviation of 6.3 and an average for the sophomores (n=30) of 79.3 with a standard deviation of 8.6. Is the claim realistic in light of the past two years?

3. A researcher recently sought to determine whether there is a noticeable difference between coronavirus infection rates among those working from home and those commuting to work in 2020. He found that out of 810 people working from home, 62 were diagnosed with COVID, and out of 656 people commuting to work, 67 were diagnosed with COVID. Is there a statistical difference between these two groups?