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

	Storm before 1995	After 1995
Mean	1.7	3.3
Variance	1.378947368	3.484211
Observations	20	20

Two variance test: To test that there is a significant difference between variances

H0: Both variances are equal

Ha: Both variances are not equal

Significance value= 0.08

df1= n1-1=19

df2=n2-1=19

The test statistic:

P-value= 0.02498

Excel Output:Using Data analysis Addin: Select F test for equality for variances:

F-Test Two-Sample for Variances
	Storm before 1995	After 1995
Mean	1.7	3.3
Variance	1.378947368	3.484210526
Observations	20	20
df	19	19
F	0.395770393
P(F<=f) one-tail	0.024987387
F Critical one-tail	0.517385156

The test statistic is significant and there is a significant difference between variances.

Two sample t-test:

H0: Both the means are equal

Ha: Less hurricanes before 1995

Using excel: Using Data analysis Addin: Select Two sample t-test for unequal variances:

t-Test: Two-Sample Assuming Unequal Variances
	before 1995	After 1995
Mean	1.7	3.3
Variance	1.378947368	3.484210526
Observations	20	20
Hypothesized Mean Difference	0
df	32
t Stat	-3.244709313
P(T<=t) one-tail	0.001376727
t Critical one-tail	1.693888703
P(T<=t) two-tail	0.002753454
t Critical two-tail	2.036933334

P-value of one tail: 0.001376

The test statistic is significant and rejects H0. There is enough evidence to support the claim that the Hurricanes increased after 1995.