Help finding:test statistic to=P value= Draw a boxplot of the differenced data. Does this visual evidence support the results obtained in part b)? A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk paintedblack and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts (a) through (c) below.Observation1246Date1/253/195/307/39/1311/7Initial Depth, X;72.170.246.450.242.355.1Depth Five Years Later, Y;79.070.151.654.048.657.6.....a) Why is it important to take the measurements on the same date?A. Using the same dates makes it easier to remember to take samples.B. Those are the same dates that all biologists use to take water clarity samples.C. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date.D. Using the same dates maximizes the difference in water clarity.b) Does the evidence suggest that the clarity of the lake is improving at the a = 0.05 level of significance? Note that the normal probability plot and boxplot of the data indicate that the differences are approximately normallydistributed with no outliers.Let d; = X; - Y;. Identify the null and alternative hypotheses.Ho: HdH1: Hd(Type integers or decimals. Do not round.)Determine the test statistic for this hypothesis test.(Round to two decimal places as needed.)

The random variable depth follows normal distribution. There are two dependent samples which are Initial Depth and Depth Five Years Later. We have to test whether clarity of the lake is improving or not. This is paired t-test with left-tailed.EXCEL (Data Analysis) Procedure: Step 1: In EXCEL sheet, enter Initial Depth in one column and enter Depth Five Years Later in one column. Step 2: In Data, select Data Analysis and choose t test: Paired Two-samples for Mean. Step 3: In Input Variable 1 Range: select Initial Depth. Step 4: In Input Variable 2 Range: select Depth Five Years Later. Step 5: Select Lables. Click Ok. EXCEL (Data Analysis) output: Test statistic, = -3.84. P-value = 0.006. Conclusion: Since p-value (=0.006) ≤α(=0.05), then reject the null hypothesis. There is sufficient evidence to conclude that clarity of the lake is improving.EXCEL output: Yes, since there is no outlier, then this visual evidence supports the results obtained in part (b).