A study was conducted to measure the effectiveness of a diet program that claims to help manage weight. Subjects were randomly selected to participate. Before beginning the program, each participant was given a score based on his or her fitness level. After six months of following the diet, each participant received another score. The study wanted to test whether there was a difference between before and after scores. What is the correct alternative hypothesis for this analysis?

Answer:x=test value before , y = test value after The system of hypothesis for this case are: Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex] Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex] If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:Null hypothesis: [tex]\mu_d = 0[/tex] Alternative hypothesis: [tex]\mu_d \neq 0[/tex] Step-by-step explanation:Previous conceptsA paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.   Let put some notation  x=test value before , y = test value after The system of hypothesis for this case are: Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex] Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex] If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:Null hypothesis: [tex]\mu_d = 0[/tex] Alternative hypothesis: [tex]\mu_d \neq 0[/tex]