Question

During the period 1990–1998 there were 46 Atlantic hurricanes, of which 20 struck the United States. During the period 1999–2006 there were 70 hurricanes, of which 46 struck the United States.

1. At α = 0.10, do the data support the hypothesis that the percentage of hurricanes that strike the United States is increasing? Follow and show the 7 steps for hypothesis testing

2. What assumption is required for this test? Show if the assumption is valid.

3. Verify with Minitab, by attaching or including the output.

Answer 1

During the period 1990–1998 there were 46 Atlantic hurricanes, of which 20 struck the United States. During the period 1999–2006 there were 70 hurricanes, of which 46 struck the United States.

Let's write the given information.

n₁ = Total number of Atlantic hurricanes during the period 1990–1998= 46

x₁ = total number of Atlantic hurricanes which struck the United States during the period 1990–1998 = 20

n₂ = Total number of Atlantic hurricanes during the period 1999–2006= 70

x₂ = total number of Atlantic hurricanes which struck the United States during the period 1999–2006 = 46

1. At α = 0.10, do the data support the hypothesis that the percentage of hurricanes that strike the United States is increasing? Follow and show the 7 steps for hypothesis testing

Here we want to test whether the data support the hypothesis that the percentage of hurricanes that strike the United States is increasing?

Let P₁ = proportion of hurricanes which struck the United States during the period 1990–1998

P₂ = proportion of hurricanes which struck the United States during the period 1999 –2006.

So the null and the alternative hypothesis are as follows:

H₀ : P₁ - P₂ = 0

H₀ : P₁ - P₂ < 0

Let's find estimates of P₁ and P₂

And the pooled estimate of proportion is as follows:

The formula of Z test statistics is as follows:

P-value = P( Z < -2.37) = 0.009

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.009 > 0.10 so we used first rule.

That is we reject the null hypothesis

Conclusion: At 10% level of significance there are sufficient evidence  that the percentage of hurricanes that strike the United States is increasing.

Look the following minitab output: