Question

1. Fictitious data—real data is available and would be interesting]

In the period 1980-2004, 8.7% of named Atlantic tropical storms were measured as “strong” hurricanes (Category 3 or higher at some point in their active “lifetime”).

As a test of one predicted effect of climate change, we want to see if this proportion has remained the same for the period 2005-2017. Assume there were 183 named Atlantic tropical storms in this period. Assume also that the 8.7% is (at least very close to) the true long-term proportion of these storms [which is the correct approach for this test].

1. What are the mean proportion and the standard deviation in that proportion for the sample of 183 storms?
2. Can we use the normal approximation for the proportion?
3. How likely would it be to find more than 10% “strong” hurricanes in the 2005-2017 period? How about 12.5%? If 12.5% of the 2005-2017 storms were strong, would you classify this as very unusual?

Answer 1

a) n = 183

p = 0.087

= p = 0.087

= sqrt(p(1 - p)/n)

     = sqrt(0.087 * (1 - 0.087)/183)

     = 0.0208

b) np = 183 * 0.087 = 15.921

   n(1 - p) = 183 * (1 - 0.087) = 167.079

Since np > 10 and n(1 - p) > 10, so we can use normal approximation.

c) P( > 0.1)

= P(( - )/ > (0.1 - )/)

= P(Z > (0.1 - 0.087)/0.0208)

= P(Z > 0.63)

= 1 - P(Z < 0.63)

= 1 - 0.7357

= 0.2643

P( > 0.125)

= P(( - )/ > (0.125 - )/)

= P(Z > (0.125 - 0.087)/0.0208)

= P(Z > 1.83)

= 1 - P(Z < 1.83)

= 1 - 0.9664

= 0.0336

Since the probability value is less than 0.05, so it is very unusual.