Hurricane frequencies
The National Hurricane Center provides data that list the numbers of large (category 3, 4, or 5) hurricanes that have struck the United States, by decade since 1851 (https://www.nhc.noaa.gov/ Deadliest_Costliest.shtml). Here are the data:
| Decade |
Count |
Decade |
Count |
| 1851-1860 |
6 |
1931-1940 |
8 |
| 1861-1870 |
1 |
1941-1950 |
10 |
| 1871-1880 |
7 |
1951-1960 |
9 |
| 1881-1890 |
5 |
1961-1970 |
6 |
| 1891-1900 |
8 |
1971-1980 |
4 |
| 1901-1910 |
4 |
1981-1990 |
4 |
| 1911-1920 |
7 |
1991-2000 |
5 |
| 1921-1930 |
5 |
2001-2010 |
7 |
Recently, there s been some concern that perhaps the number of large hurricanes has been increasing. The natural null hypothesis would be that the frequency of such hurricanes has remained constant.
a) With 96 large hurricanes observed over the 16 periods, what are the expected value(s) for each cell? b) What kind of chi-square test would be appropriate?
c) State the null and alternative hypotheses. d) How many degrees of freedom are there?
e) The value of χ2 is 12.67. What's the P-value of the test?
f) State your conclusion.
g) Look again at the definition of the last decade. Does that alter your conclusion at all?