Question

During the period 1990–1998 there were 46 Atlantic hurricanes, of which 19 struck the United States. During the period 1999–2006 there were 70 hurricanes, of which 45 struck the United States.

(a-1) Does this evidence convince you that the percentage of hurricanes that strike the United States is increasing, at α = .01? Let ππ ₁ = proportion of hurricanes in United States from 1990-1998 and ππ ₂ = proportion of hurricanes in United States from 1999-2006. Choose the correct null and alternative hypotheses.

H₀: ππ ₁ –  ππ ₂ ≤ 0 vs. H₁: ππ ₁ –  ππ ₂ > 0

H₀: ππ ₁ –  ππ ₂ = 0 vs. H₁: ππ ₁ –  ππ ₂ ≠ 0

H₀: ππ ₁ –  ππ ₂ ≥ 0 vs. H₁: ππ ₁ –  ππ ₂ < 0

a

b

c

(a-2) Identify the decision rule.

Reject the null hypothesis if z_calc < –2.33

Reject the null hypothesis if z_calc > –2.33

a

b

(a-3) Calculate the z test statistic value. (A negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

Value of the test statistic, z_calc           

(a-4) Calculate the p-value. (Round your answer to 4 decimal places.)

p-value           

(a-5) Does this evidence convince you that the percentage of hurricanes that strike the United States is increasing, at α = .01?

Yes

No

(b) Can normality be assumed?

Yes

No

Answer 1

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions
H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ < 0

Hypothesis test results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	Z-Stat	P-value
p1 - p2	19	46	45	70	-0.22981366	0.0943919	-2.4346757	0.0075

Hence,

a - 1) Option C is correct.

a - 2) Option A is correct.

a - 3) z = -2.435

a - 4) p - Value = 0.0075

a - 5) Yes

b) Yes