homework helpWhat is t0=what is p value= In this study, a researcher investigates water clarity at a consistent location in a lake. The research involves recording measurements on identical dates over two separate years, spaced five years apart. The procedure utilizes a weighted disk painted black and white to measure the depth (in inches) at which it becomes invisible. The data collected is tabulated below:| Observation | 1 | 2 | 3 | 4 | 5 | 6 ||-------------|----|----|----|----|----|----|| Date | 1/25 | 3/19 | 5/30 | 7/3 | 9/13 | 11/7 || Initial Depth, \( X_i \) | 65.9 | 74.2 | 70.7 | 66.6 | 69.8 | 50.3 || Depth Five Years Later, \( Y_i \) | 73.4 | 73.5 | 65.4 | 70.4 | 76.7 | 52.0 |**Tasks:**- **a) Formulate the Null Hypothesis (\( H_0 \)) and Alternative Hypothesis (\( H_4 \)):** \((Type integers or decimals. Do not round.)\)- **b) Determine the test statistic for this hypothesis test:** \((Round to two decimal places as needed.)\)Instructions for students: Analyze the data to consider changes in water clarity over the five years, using appropriate statistical methods to test the stated hypotheses.

This is a pair test. sample size (n) = 6 mean (d̄) = Σd/n = -23.9/6 = -3.98 Standard deviation (Sd) = √ (d-d̄)2 /(n-1) = √ 48.5684/(6-1) = 3.1167 Test statistic = (d̄ -μd)/(Sd/√n) = (-3.98-0)/( 3.1167/√6) = -3.1280 ≈ -3.13 degree of freedom (df) = n- 1 = 6-1 = 5 significance level α = 0.05 For a one tailed test , p -value = 0.012979 (from t distribution table)