8. A soccer coach uses a new technique to get his players to run faster. 7 players were randomly selected and their running times (in seconds) for a 50m dash were recorded before and after the new training technique. The results are: Player number 1 2 3 4 5 6 7 Time Before Training 10312.1 12.312.1 13.812.012.6 Time After Training 9.8 11112012613212.8115 Differences (use Before After) The coach wants to test the claim that the mean running time for all players will improve after using the new training. Assume that the differences in running times for players are normally distributed, and use a 10% level of significance. a. For this test, write the appropriate null hypothesis and alternative hypothesis for the population mean of the differences In running times. Use table. b. Calculate the differences in times for each person and fill in the table above. 0. Using your calculator, nd the following sample statIsucs for the differences in times (round to 3 decimal places where necessary): d. Determine the T test-statistic. Round to 3 decimal places. e. Determine the P-value. Round to 3 decimal places. f. At a 5% level of significance, what are the conclusions about and ? 9. Write the conclusion the coach can make in the context of the