3) The following data was obtain testing students' reaction times (in Milliseconds) on a driving skills test either using or not using a cell phone simultaneously during the test . Assume that reaction time is normally distributed in the population . (7 pts ) Studen With Without + Difference Phone Phone 636 86 38 623 556 67 615 40 75 4 672 522 150 5 601 459 142 619 33 86 542 513 29 554 470 84 543 56 -13 10 520 531 -11 11 609 599 10 12 559 537 22 13 595 607 -12 14 565 36 29 15 573 19 16 554 467 87 Mean 586.25 536.13 50.13 Stdev 41.28 44.57 51.06 Run the appropriate test to determine if student reactions are different during the test when they are using a phone compared to when they are not. Use a t-critical of 2.131. What are the null hypothesis (H ) and alternative hypothesis (H )? b. Calculate the appropriate test statistic for this test. Show your work. c. What is your answer to the question: did student react slower during the test using the phone? Include statistics in your answer. d. If the researchers conducted this test again with the same size sample and obtained the same mean of the difference, but this time achieved a standard deviation of the difference double what they found the first time (s=102.12), which value(s) would change from the conclusion? How would the value(s) change (would they be larger or smaller)? Would your conclusion change? e. Rewrite the new conclusion including your new t-statistic from part d