News of your analytical prowess has spread throughout the area. Naturally, when the coaching staff of your teen’s high school lacrosse team has a statistical question, they contact the best: you. The coaching staff wants to know if they can be 95% confident (which means α = 0.05) that the average difference between the home team and their opponent is more than +2 points. Use the data below from 35 randomly chosen games to answer their question. The home team’s scores are listed first.12 – 67 – 510 – 45 – 69 – 87 – 57 – 28 – 68 – 28 – 47 – 18 – 56 – 413 – 510 – 45 – 89 – 66 – 55 – 410 – 67 – 1014 – 107 – 26 – 56 – 57 – 68 – 78 – 39 – 88 – 610 – 410 – 96 – 78 – 18 – 5What is the name of the type of hypothesis test required here?Is this a left-tailed, right-tailed, or two-tailed test?State AND verify all assumptions required for this test. State the null and alternate hypotheses for this test: (use correct symbols and format!) Null hypothesisAlternate hypothesisRun the correct hypothesis test and provide the information below. Give the correct symbol AND numeric value of each of the following (round answers to 3 decimal places).Test StatisticCritical value [HINT: this is NOT αM6tK0A1AZ4oEWQ1oRRJAGIQ1DlY7AYJocf dnYnxB ]Degrees of Freedomp-valueState your statistical decision (and justify it!)Interpret your decision within the context of the problem: what is your conclusion?