Chapter 14, Problem 14.1.1RE

Hurricanes Select a random sample of eight storms by using random numbers, and find the average maximum wind speed. Compare with the population mean.

Wind Speed of Hurricanes

The 2015 Atlantic hurricane season was notable for many reasons, among them the most named storms and the most hurricanes. Use the data shown to answer questions 1 through 4.

To determine

The average maximum wind speed

To compare: The results with the population mean.

Answer to Problem 14.1.1RE

The average maximum wind speed is 97.5

By comparing the means it is clear that there is larger difference between the sample mean and the population mean

Explanation of Solution

Calculation:

First arrange the data according to the serial number,

SNO	Name	Max. wind	Classification	Atlantic/pacific
1	Ana	60	S	A
2	Bill	60	S	A
3	Claudette	50	S	A
4	Danny	115	H	A
5	Ela	45	S	P
6	Erika	50	S	A
7	Fred	85	H	A
8	Grace	50	S	A
9	Guillerma	105	H	P
10	Halola	65	S	P
11	Henri	50	S	A
12	Hilda	140	H	P
13	Ida	50	S	A
14	Ignacio	145	H	P
15	Iune	40	S	P
16	Jimena	120	H	P
17	Joaquin	155	H	A
18	kate	75	H	A
19	Kilo	140	H	P
20	Loke	75	H	P
21	Malia	40	S	P
22	Naila	65	S	P
23	oho	95	H	P

$\text{S}=\text{Storm, H}=\text{Hurricane, A}=\text{Atlantic and P}=\text{Pacific}$

From the data select a random sample of eight storms by using random numbers.

Procedure for selecting eight random samples:

• From the figure 14.1(Table of random numbers), select a starting point.
• Here, the selected starting point is ‘18’ which is present in third row and first column. There are 23 names of storms. Hence; select the random numbers in the range of ‘1’ to ‘23’. Avoid repetition of numbers and 00.
• The random numbers starting from ‘18’ are,

  18,19,14,29,01,55,84,62,66,48,94,100,46,77,81,40,41,52,13,82,57,12,27,75,95,62,57,13,31,06,16

• Select 18, 19,14 which are in the range (01 to 23).
• Next number 29 is not selected because it is not in the range (1 to 23).
• And select 01.
• Repeat the same until eight random numbers are obtained.
• Thus, the random numbers are and corresponding names of the wind are,

S NO	NAME
01	Ana
06	Erika
12	Hilda
13	Ida
14	Ignacio
16	Jimena
18	Kate
19	kilo

The average maximum wind of above selected sample is calculated by using the following formula.

$\begin{array}{c}\text{Sample mean of Max}.\text{wind speed} =\frac{\text{Sum}\text{of}\text{all}\text{sample}\text{values}\text{of}\text{Max}\text{.wind}}{\text{Number}\text{of}\text{samples}}\\ =\frac{60+50+140+50+145+120+75+140}{8}\\ =\frac{780}{8}\\ =97.5\end{array}$

Thus, the sample mean is 97.5

The population mean of maximum wind is,

$\begin{array}{c}\text{Population mean} =\frac{\text{Sum}\text{of}\text{all}\text{values}\text{of}\text{Max}\text{.wind}}{\text{Number}\text{of}\text{obervations}}\\ =\frac{60+60+50+115+\mathrm{...}+65+95}{23}\\ =\frac{1,875}{23}\\ =81.52\end{array}$

Comparison of means:

The sample mean of maximum wind speed is 97.5and the population mean of maximum wind speed is 81.52.

That implies that the sample mean is larger than the population mean.It is clear that there is larger difference between the sample mean and the population mean.