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There is substantial evidence to indicate that temperatures on the surface of the Earth have been increasing for the past 100 years or so. We will investigate the possibility of warming trends in one location: Washington, D.C. Table 9.4 presents the record high and low temperatures, along with the year they occurred, for every seventh day at the site of Reagan National Airport in Washington, D.C. The data span the years 18712018.

1. If there have been no temperature trends over the years, then it will be equally likely for the record high or the record low to be more recent. If there has been a warming trend, it is more likely for the record high to be more recent. Let be the probability that the record high occurred more recently than the record low. a. Find the sample proportion of dates where the high occurred more recently. Be sure to use correct notation. (Remember, represents the sample proportion.) b. To determine whether there is evidence that record highs occur more recently than record lows, test the hypothesis that o: = 0.5 versus 1: 0.5 using the = 0.05 level of significance. (Be sure to check assumptions, perform the test, state the pvalue, and whether the null hypothesis is rejected or not.) c. Based on the test performed in part b), what is your conclusion about whether there has been a warming trend? (Best to use language like: Based on a pvalue of ___, there is evidence that or Based on a pvalue of ___, there is not sufficient evidence that .)

Date Low Year Date Low Year Date Low Year High Year 69 2005 Jan 1 More Recent Low -14 More Recent High High 1881 High Year 95 1930 93 1956 May 7 38 1970 High Year 98 1953 98 1983 Sep 3 10 1909 More Recent High High 8 73 2008 0 1878 14 41 1928 44 1883 15 77 1932 4 1886 21 1934 41 1907 High High Low 17 96 1991 44 95 97 1923 22 76 1927 1 1893 28 1941 42 1961 24 99 2010 39 1963 High High High High 29 76 1975 2 High High High High High 1873 Jun 4 99 1925 46 1929 Low Oct 1 93 1941 36 1899 Feb 5 70 1991 -2 1918 11 101 1911 45 1913 Low 8 91 2007 36 1964 12 74 1999 1899 18 97 1944 51 1965 Low 15 1975 1874 High 32 29 19 74 1939 4 1903 High 25 100 1997 1902 22 84 1979 1895 High 53 55 26 74 1932 1970 Low Jul 2 101 1898 1940 29 82 1918 30 1976 Low 12 6 Mar 5 83 1976 1872 9 104 1936 55 1891 Nov 5 81 2003 20 1879 12 89 1990 11 1900 High High High 16 104 1988 1930 12 77 1912 24 1926 56 56 High Low High High 19 87 1945 12 1876 23 102 2011 1890 19 77 1928 18 High Low High High High High High High High High 1891 26 87 1921 23 1955 Low 30 99 1953 56 1914 26 74 1979 17 1950 Apr 2 89 1963 23 1907 High 106 1918 53 1912 Dec 3 71 2012 15 1976 High Aug 6 13 9 90 1959 28 1972 Low 2016 55 1930 10 67 1966 4 1876 High 101 101 16 92 2002 29 1928 20 1983 50 1896 17 64 1984 10 1876 High High 23 95 1960 33 High High High 1933 27 100 1987 51 1885 24 71 2015 5 1983 30 92 1942 34 1874 Date Low Year Date Low Year Date Low Year High Year 69 2005 Jan 1 More Recent Low -14 More Recent High High 1881 High Year 95 1930 93 1956 May 7 38 1970 High Year 98 1953 98 1983 Sep 3 10 1909 More Recent High High 8 73 2008 0 1878 14 41 1928 44 1883 15 77 1932 4 1886 21 1934 41 1907 High High Low 17 96 1991 44 95 97 1923 22 76 1927 1 1893 28 1941 42 1961 24 99 2010 39 1963 High High High High 29 76 1975 2 High High High High High 1873 Jun 4 99 1925 46 1929 Low Oct 1 93 1941 36 1899 Feb 5 70 1991 -2 1918 11 101 1911 45 1913 Low 8 91 2007 36 1964 12 74 1999 1899 18 97 1944 51 1965 Low 15 1975 1874 High 32 29 19 74 1939 4 1903 High 25 100 1997 1902 22 84 1979 1895 High 53 55 26 74 1932 1970 Low Jul 2 101 1898 1940 29 82 1918 30 1976 Low 12 6 Mar 5 83 1976 1872 9 104 1936 55 1891 Nov 5 81 2003 20 1879 12 89 1990 11 1900 High High High 16 104 1988 1930 12 77 1912 24 1926 56 56 High Low High High 19 87 1945 12 1876 23 102 2011 1890 19 77 1928 18 High Low High High High High High High High High 1891 26 87 1921 23 1955 Low 30 99 1953 56 1914 26 74 1979 17 1950 Apr 2 89 1963 23 1907 High 106 1918 53 1912 Dec 3 71 2012 15 1976 High Aug 6 13 9 90 1959 28 1972 Low 2016 55 1930 10 67 1966 4 1876 High 101 101 16 92 2002 29 1928 20 1983 50 1896 17 64 1984 10 1876 High High 23 95 1960 33 High High High 1933 27 100 1987 51 1885 24 71 2015 5 1983 30 92 1942 34 1874