472 Chapter 9 Hypothesis Testing a. State the null and alternate hypotheses. H0 : �� = 1000, H1: �� > 1000 b. Should we perform a z-test or a t-test? Explain. t-test c. Compute the value of the test statistic. 2.108 d. Do you reject H0? Use the �� = 0.05 level. Yes e. State a conclusion. 15. What’s the news? The Pew Research Center reported in 2012 that 23% of 18- to 29-year-olds watch a cable news channel regularly. The director of media relations at a large university wants to know whether the population proportion of cable news viewers among students at her university is greater than the proportion among 18- to 29-year-olds in general. She surveys a simple random sample of 200 students at the university and finds that 66 of them watch cable news regularly. Can she conclude that the proportion of students at her university who watch cable news regularly is greater than 0.23? a. State the null and alternate hypotheses. H0 : p = 0.23, H1: p > 0.23 b. Compute the value of the test statistic. 3.36 c. Do you reject H0? Use the �� = 0.01 level. Yes d. State a conclusion. Write About It 1. A result is significant at the 0.01 level. Explain why it must also be significant at the 0.05 level. 2. What does the P-value represent? 3. Why is it important to report the P-value or the test statistic when presenting the results of a hypothesis test? 4. Why don’t we need to know the population standard deviation when performing a test about a population proportion? 5. In what ways are hypothesis tests for a population mean different from hypothesis tests for a proportion? In what ways are they similar? 6. A test will be made of H0 : �� = 12 versus H1: �� > 12. Explain why the power will be greater when the true value of �� is 20 than when the true value of �� is 15. Case Study: Is It Getting Warmer In Washington, D.C.? 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 1871–2013. Table 9.4 Dates of Record Temperatures in Washington, D.C. More More More Date High Year Low Year Recent Date High Year Low Year Recent Date High Year Low Year Recent Jan 1 69 2005 −14 1881 High May 7 95 1930 38 1970 Low Sep 3 98 1953 48 1909∗ High 8 73 2008 0 1878 High 14 93 1956 41 1928 High 10 98 1983 44 1883 High 15 77 1932 4 1886 High 21 95 1934 41 1907 High 17 96 1991 44 1923 High 22 76 1927 1 1893 High 28 97 1941 42 1961 Low 24 99 2010 39 1963 High 29 76 1975 2 1873 High Jun 4 99 1925 46 1929∗ Low Oct 1 93 1941∗ 36 1899 High Feb 5 70 1991∗ −2 1918∗ High 11 101 1911 45 1913 Low 8 91 2007 36 1964∗ High 12 74 1999 4 1899 High 18 97 1944 51 1965∗ Low 15 87 1975 32 1874 High 19 74 1939 4 1903 High 25 100 1997 53 1902 High 22 84 1979∗ 29 1895 High 26 74 1932 12 1970 Low Jul 2 101 1898 55 1940 Low 29 82 1918 30 1976∗ Low Mar 5 83 1976 6 1872 High 9 104 1936 55 1891 High Nov 5 81 2003∗ 20 1879 High 12 89 1990 11 1900 High 16 104 1988 56 1930∗ High 12 77 1912∗ 24 1926 Low 19 87 1945 12 1876 High 23 102 2011 56 1890 High 19 77 1928 18 1891 High 26 87 1921 23 1955 Low 30 99 1953 56 1914 High 26 74 1979 17 1950 High Apr 2 89 1963 23 1907 High Aug 6 106 1918 53 1912 High Dec 3 71 2012 15 1976 High 9 90 1959 28 1972∗ Low 13 101 1881 55 1930∗ Low 10 67 1966∗ 4 1876 High 16 92 2002 29 1928 High 20 101 1983 50 1896 High 17 64 1984∗ 10 1876 High 23 95 1960 33 1933∗ High 27 100 1987 51 1885 High 24 69 1933 5 1983 Low 30 92 1942∗ 34 1874 High ∗Indicates that the record occurred more than once; only the most recent year is given. Source: National Weather Service
navidi_monk_elementary_statistics_2e_ch7-9
To see the actual publication please follow the link above