Question

1. It has been suggested that global warming may increase the frequency of hurricanes. The table given below shows the number of major Atlantic hurricanes recorded annually before and after 1990.

before 1995		after 1995
year	# of storms	year	# of storms
1976	2	1996	6
1977	1	1997	1
1978	2	1998	3
1979	2	1999	5
1980	2	2000	3
1981	3	2001	4
1982	1	2002	2
1983	1	2003	3
1984	1	2004	6
1985	3	2005	7
1986	0	2006	2
1987	1	2007	2
1988	3	2008	5
1989	2	2009	2
1990	1	2010	5
1991	2	2011	4
1992	1	2012	2
1993	1	2013	0
1994	0	2014	2
1995	5	2015	2

Does this data is sufficient enough to claim that the number of annual hurricanes increased since 1995? Do the test at 8% significance level. To do the test, answer the following: a. Write down the null and alternative hypotheses. b. Get the excel output and answer the following: i. Fill the cell with the p-value of the test with green color ii. Fill the cell with the test statistic of the test with yellow color

Answer 1

(a)

Hypotheses are:

(b)

Here we need to use independent sample t test. Following is the output generated by excel:

Hypothesis Test: Independent Groups (t-test, unequal variance)
	X1	X2
	1.70	3.30	mean
	1.17	1.87	std. dev.
	20	20	n
		32	df
		-1.600	difference (X1 - X2)
		0.493	standard error of difference
		0	hypothesized difference
		-3.24	t
		.0028	p-value (two-tailed)
	F-test for equality of variance
		3.48	variance: X2
		1.38	variance: X1
		2.53	F
		.0500	p-value

The p-value is: 0.0028

The test statistics is t = -3.24

Since p-value is less than 0.08 so we reject the null hypothesis at  8% significance level.. That is this data is sufficient enough to claim that the number of annual hurricanes increased since 1995.