Using the data below ( Year & Flow ), develop a histogram; a probability plot, a

Question

Using the data below ( Year & Flow ), develop a histogram; a probability plot, and use chi-square goodness-of-fit test against normal distribution. Based on the analysis, state your conclustion.

Please provide a detailed response, it will be vary helpful. If you are using a software to plot. please provide a title of the software and any commands used to reach your answer. Again , the more detail the easyier it will be for me to understand your answer and check your work . Thank you ! : -^)

Year

1895

Flow (Cfs)

47300

Year

1895

Flow (Cfs)

47300

1896 54400 1897 87200 1898 65700 1899 91500 1900 53500 1901 67800 1902 70000 1903 66900 1904 34700 1905 58000 1906 47000 1907 66300 1908 80900 1909 80000 1910 52300 1911 58000 1912 67200 1913 115000 1914 46100 1915 52400 1916 94300 1917 111000 1918 71700 1919 96100 1920 92500 1921 34100 1922 69000 1923 73400 1924 99100 1925 79200 1926 62600 1927 93700 1928 68700 1929 80100 1930 32300 1931 43100 1932 77000 1933 53600 1934 70800 1935 89400 1936 62600 1937 112000 1938 44000 1939 84300 1940 45000 1941 28400 1942 46000 1943 80400 1944 55000 1945 72900 1946 71200 1947 46800 1948 84100 1949 61300 1950 87100 1951 70500 1952 77700 1953 44200 1954 20600 1955 85000 1956 82900 1957 88700 1958 60200 1959 40300 1960 50500 1961 48800 1962 101000 1963 63800 1964 82500 1965 60300 1966 38900 1967 69900 1968 55200 1969 29400 1970 68400 1971 51700 1972 107000 1973 58600 1974 77900 1975 79600 1976 46300 1977 53400 1978 61800 1979 144000 1980 40600 1981 49600 1982 42900 1983 68800 1984 98400 1985 36500 1986 42100 1987 35100 1988 105000 1989 53600 1990 82900 1991 54600 1992 52100 1993 71000 mean 66538.38 stdev 22320.22

Explanation / Answer

Using R-software

Flow=c(47300,54400,87200,65700,91500,53500,67800,70000,66900,34700,58000,47000,66300,80900
,80000,52300,58000,67200,115000,46100,52400,94300,111000,71700,96100,92500,34100,69000,73400
,99100,79200,62600,93700,68700,80100,32300,43100,77000,53600,70800,89400,62600,112000,44000
,84300,45000,28400,46000,80400,55000,72900,71200,46800,84100,61300,87100,70500,77700,44200,
20600,85000,82900,88700,60200,40300,50500,48800,101000,63800,82500,60300,38900,69900,55200,
29400,68400,51700,107000,58600,77900,79600,46300,53400,61800,144000,40600,49600,42900,68800,
98400,36500,42100,35100,105000,53600,82900,54600,52100,71000)
hist(Flow, main="Histogram of Flow (Cfs)")

Using Excel

So, we reject the hypothesis.

Up to Freq P(x<=b) P(a<x<=b) Exp freq (O-E)^2/E 20000 0 0.018533 0.018533 1.834785 1.834785 40000 9 0.117223 0.09869 9.770294 0.06073 60000 32 0.384786 0.267563 26.48872 1.146686 80000 31 0.726783 0.341998 33.85775 0.241208 100000 20 0.933084 0.206301 20.42378 0.008793 120000 6 0.991695 0.05861 5.802432 0.006727 140000 0 0.999501 0.007807 0.772865 0.772865 160000 1 0.999986 0.000485 0.047974 18.89257 98.9986 21.12958 degree of freedom 7 X2-crit 14.0671

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