A physics lab believes it has developed a more efficient gain medium to produce a laser of greater power at a reduced energy cost, but they need to verify this before they publish their results. They take 30 observations each on the power output from their new laser and a current laser and compare the difference in the average outputs. The sample estimate for this difference in average power outputs comes to 0.095.a) What type of test would they conduct in this situation?Goodness of fit testTwo-sample t-test Test of independenceTwo-sample proportion testPaired t-test b) If they were going to conduct this hypothesis test, given that their standard error was 0.012, what would be the value of the test statistic? Use 3 decimal places.