Researchers at a university designed and tested a​ speed-training program for junior varsity and varsity high school football players. Each in a sample of 38 high school athletes was timed in a​ 40-yard sprint prior to the start of the training program and timed again after completing the program. The decreases in times​ (measured in​ seconds) are listed in the accompanying table.​ [Note: A negative decrease implies that the​ athlete's time after completion of the program was higher than his time prior to​ training.] The goal of the research is to demonstrate that the training program is effective in improving​ 40-yard sprint times. Use these data to complete parts a and b below.

Acell phone company offers two plans to its subscribers. at the time new subscribers sign up, they are asked to provide some demographic information. the mean yearly income for a sample of 40 subscribers to plan a is $45,000 with a standard deviation of $9,200. for a sample of 25 subscribers to plan b, the mean income is $64,300 with a standard deviation of $7,100. at the 0.025 significance level, is it reasonable to conclude the mean income of those selecting plan b is larger? assume unequal population standard deviations. hint: for the calculations, assume the plan a as the first sample. what is the decision rule? (negative amount should be indicated by a minus sign. round your answer to 3 decimal places.) compute the value of the test statistic. (negative amount should be indicated by a minus sign. round your answer to 2 decimal places.) what is your decision regarding h0 ? reject h0 fail to reject h0 compute the p-value. less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10