1.The number of cars passing eastbound through the intersection of Mill and University Avenues has been tabulated by a group of civil engineering students. They have obtained the data in the adjacent table.Vehiclesper MinuteObservedFrequencyVehiclesper MinuteObservedFrequency4014531024124549642575590431115681441945773452565864462965961473786059482506150491856242501716329511506418521106515 In this problem, you’ll be testing whether the above data reflects a Poisson distribution.a.Derive the maximum likelihood estimator for a Poisson Distribution with parameter l.b.Using your answer from part 1, if we assume the data does reflect a Poisson Distribution, find the estimator for l.c.Create an appropriate histogram of the data. Use as many buckets as you think is appropriate.d.Using the results from parts (2) and (3), and the provided data, run an appropriate test to determine whether the data comes from a Poisson Distribution.2.Consider the data below.Hours Studied1031.52.7510.5231.75Test Score7666968410081857910081a.Using Least-Squares regression, find the line of best fit that uses Hours Studied to predict a Test Score.b.Create a scatterplot of the data and draw your line from part (a). c.Find SSE, SSR, and SST.d.Find the Coefficient of Determination, and give a brief interpretation of the answer.e.Test whether both the intercept and slope parameters are 0. Use α = 0.05f.We define regression correlation as, where XY is the covariance between Y and X.It can be determined that, and a correlation is considered Strong if |is above .5. In other words, the sample correlation coefficient is the square root of R2. Find the sample correlation. g. Run an appropriate test to determine whether this correlation is 0. The test statistic, , has degrees of freedom n-2.3. Two different analytical tests can be used to determine the impurity level in steel alloys. Eight specimens are tested using both procedures, and the results are shown in the following tabulation. Is there sufficient evidence to conclude that both tests give the same mean impurity level, using α = 0.01? Round numeric answer to 2 decimal places.SpecimenTest 1Test 211.41.621.51.931.71.741.41.351.92.2622.371.61.981.51.84.Consider the data from problem (3). If we could not assume the data came from a paired test, would you reach the same conclusion? Run an appropriate Hypothesis test with α = 0.01.
