CIV3204 - Engineering Investigation Assignment Questions

Assignment Help Basic Statistics

Reference no: EM132381295

CIV3204 - Engineering Investigation Assignment Questions, 2019 SEMESTER 2, Monash University, Australia

The assignment for this subject consists of the analysis of stream flow and rainfall data for the Woori Yallock catchment in Victoria. The coordinates of the outlet for this catchment are:

Latitude: -37.76

Longitude: 145.51

Figure 2.1 (attached) shows the outline of the catchment. In the first part of the assignment, the required data need to be downloaded and processed. The second part of the assignment consists of fitting a probability distribution. In the third part, the sampling distribution will be fitted, and some inferences regarding the properties of the data will be made. The fourth and last part will focus on an analysis of a number of linear regressions of the data.

For each part of the assignment, your report should outline how you performed the calculations, and the steps you took to come to your conclusions.

Table 2.1: List of years to analyze for Assignments 1 and 2 depending on the student ID number.
Last digit student ID number	First five years	Second five years	Third five years
0	1969-1973	1988-1992	2005-2009
1	1970-1974	1989-1993	2006-2010
2	1971-1975	1990-1994	2007-2011
3	1972-1976	1991-1995	2008-2012
4	1973-1977	1992-1996	2009-2013
5	1974-1978	1993-1997	2010-2014
6	1975-1979	1994-1998	2011-2015
7	1976-1980	1995-1999	2012-2016
8	1977-1981	1996-2000	2013-2017
9	1978-1982	1997-2001	2014-2018

2.1 Data Analysis -

Download the stream flow data for the test site.

Download as many years as possible.

Download the daily rainfall data for the nearest rainfall station with a sufficiently long time series, which is Coranderrk Badger Weir. Again, download as many years as possible.

We will work with full years of data, thus from 1969 through 2018.

Important: For this part of the assignment, as well as for part 2, we will work with the logarithms of the nonzero flows.

First, use three sets of five consecutive years (for example 1976 through 1980), making sure the three sets do not overlap. Table 2.1 lists the years to analyze depending on your student ID number. These sets of years are roughly covering the beginning, middle, and end of the time series, respectively. Calculate the mean, standard deviation, and skewness for the stream flow each of the three sets. Calculate the same statistics for one year in each of the three sets. Comparing the one year to the five year statistics, are there any conclusions you can draw?

Table 2.2: Year to perform a Gaussian probability plot for, depending on the student id number.
Last digit student id number	Year to analyze
0	2009
1	2010
2	2011
3	2012
4	2013
5	2014
6	2015
7	2016
8	2017
9	2018

2.2 Probability and Distribution Fitting

For the same data sets as in the first part of the assignment, we will check whether or not the stream flow data follow a lognormal distribution (in other words, if the logarithms of the data follow a Gaussian distribution). We will apply a χ² test for this purpose, with 5% significance. What conclusions can you draw from this analysis?

We will also test the Gaussianity of the logarithms of the flows through a Gaussian probability plot, as explained in slides 29 and 30 in week 4. Table 2.2 shows the year that you must analyze, depending on your student id number. What do you conclude from this analysis?

Through a routine water quality analysis, it is found that somebody has illegally dumped paint in the river. This paint has been found downstream of an area with50houses.Thismeansthatany of these 50 houses could have polluted the water. Through analyzing the houses, a consultant has determined that there is an 90% chance that the paint used by household A is the paint that is found in the water. Does this mean that there is an 90% chance that household A is guilty of polluting the stream? If yes, explain your reasoning. If not, calculate the chance that the household is guilty, and explain your reasoning.

The council decides to perform a water quality check every day. This test costs $500 each day. If a pollutant is found in the water, they assume that they will find the pollutor, and they will fine them $50,000. What does the probability to find a pollutant in the sample each day at least have to be, for the council to be 90% sure that they will not lose money on these tests, in a non-leap year?

The council is contemplating organizing nature walks along the river with a paid guide. The walks last for a day, and the guide charges $50 per customer per day. The salary of the guide is $1100 per week, and he is expected to guide at least 25 people per week. How certain can the council be that they will be cash-flow positive any random week?

Table 2.3: List of years to analyze for Assignment 3 depending on the student ID number. L2D stands for the last two digits of your student ID number.
L2D	Year	L2D	Year	L2D	Year	L2D	Year	L2D	Year
00	1969	01	1970	02	1971	03	1972	04	1973
05	1974	06	1975	07	1976	08	1977	09	1978
10	1979	11	1980	12	1981	13	1982	14	1983
15	1784	16	1985	17	1986	18	1987	19	1988
20	1789	21	1990	22	1991	23	1992	24	1993
25	1994	26	1995	27	1996	28	1997	29	1998
30	1999	31	2000	32	2001	33	2002	34	2003
35	2004	36	2005	37	2006	38	2007	39	2008
40	2009	41	2010	42	2011	43	2012	44	2013
45	2014	46	2015	47	2016	48	2017	49	2018
50	1969	51	1970	52	1971	53	1972	54	1973
55	1974	56	1975	57	1976	58	1977	59	1978
60	1979	61	1980	62	1981	63	1982	64	1983
65	1784	66	1985	67	1986	68	1987	69	1988
70	1789	71	1990	72	1991	73	1992	74	1993
75	1994	76	1995	77	1996	78	1997	79	1998
80	1999	81	2000	82	2001	83	2002	84	2003
85	2004	86	2005	87	2006	88	2007	89	2008
90	2009	91	2010	92	2011	93	2012	94	2013
95	2014	96	2015	97	2016	98	2017	99	2018

2.3 - Sampling Distributions

Important: From here on, we work with the raw observations, thus no longer with the logarithms of the nonzero flows.

Table 2.3 lists the year to analyze depending on your student ID number. From the data in that year, take a sample of 100 random discharge observations (with replacement) and calculate the mean. Repeat this 100 times. Plot the distribution of these sample means, and compare to the theoretical sampling distribution. Do the same exercise with 200 and 1000 repetitions. What can you conclude about the obtained distributions?

Assume you have one day with 24 observations. What is the probability that the daily average is going to be larger than 0.5, 1, 2 and 3 m³s^-1?

We want to check whether or not the annual averaged stream flow has changed over the years. We will use an ANOVA for this purpose. We will work with annual averages of the stream flow data. The years 1970-1979 are assumed treatment 1, the years 1980-1989 treatment 2, the years 1990-1999 treatment 3, and the years 2000-2009 treatment 4. Check at the 5 and 10% significance levels if the averages for the four decades are different or not. If there are differences, use the Tukey-Kramer procedure to check which decades are different from each other.

We also want to test whether the variability of the time series has changed over the years. Pick a random year in the first five years of the time series, and another in the last five years of the time series. Check if there is a difference at the 5% significance level. Does this change at the 1% significance level?

Note - Section 2.3 is required to be completed. It is statistics regarding ANOVA.

Attachment:- Engineering Investigation Assignment File.rar

Reference no: EM132381295

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