79130524 Employees In The Fashion Designers Industry

Fashion designers:				Stem and leaf
Introduction:				14
This paper analysis the income levels of				42
employees in the fashion designers industry, this				20
industry according to the bureau of labour in the				22
United States it is estimated that this industry				24
employs over 20,000 individuals according to the				50
year 2006 statistics. This industry mainly focuses				25
on dress making, clothing, shoes of different				47
styles and making.				68
Data on the income levels of employees in the				27
fashion industry was retrieved from the bureau				19
of statistics in the US				07
The data:				33
Data was retrieved the data contains				64
employment levels in these states, hourly wage				03
rate and the mean annual income in terms of				03
wage, the data below shows the data:				29
Area name				49
Employment				80
Hourly mean wage				61
Annual mean wage(2)				30
Los Angeles-Long Beach-Glendale, CA Metropolitan				87
Division				88
2500				31
34.34				12
71430				0
Los Angeles-Long Beach-Santa Ana, CA				32
2920				01
33.66				07
70010				33
Riverside-San Bernardino-Ontario, CA				66
30				80
27.19				34
56560				34
San Francisco-Oakland-Fremont, CA				36
240				25
36.25				37
75400				70
San Francisco-San Mateo-Redwood City, CA				28
Metropolitan Division				71
150				70
33.8				22
70310				The above is the stem and leaf representation of
Santa Ana-Anaheim-Irvine, CA Metropolitan				the data, it is clear that most of the observation
Division				are in the wage rate 27, this data therefore is
410				skewed to the left and does not assume a
29.49				normal distribution.
61350				Binomial probability distribution:
Washington-Arlington-Alexandria, DC-VA-MD-WV				The binomial probability distribution is applied to
30				find the probability that an outcome will occur in a
27.07				given number of trials. The variable in this case
56300				however must be a discrete dichotomous random
Boston-Cambridge-Quincy, MA-NH				variable, in this distribution we consider n identical
680				trials, each trial has two possible outcomes where
29.8				we refer to a success and the other as a failure,
61990				a success in our case will be denoted as P and a
Boston-Cambridge-Quincy, MA NECTA Division				failure will be denoted as Q. finally the outcome of
450				one trial does not affect the outcome of the
29.61				other trial,
61600				In our case we will construct the binomial
Brockton-Bridgewater-Easton, MA NECTA Division				probability distribution using the statement that
60				the employment level in the fashion and design
27.33				industry is expected to grow by 5%, assuming
56850				that our level of employment in our selected
Providence-Fall River-Warwick, RI-MA				states is 12,000 then we expect that in 2016 the
50				employment level will be 70,000.
24.5				According to this statistics the employment level
50970				is based on a 2006 report and therefore the time
Minneapolis-St. Paul-Bloomington, MN-WI				period is 10 years, which also means 120 months,
90				so employment level is expected to increase by 5
27.64				individual each month. This statistics were
57490				retrieved . if now we assume that the probability
Allentown-Bethlehem-Easton, PA-NJ				of this happening is 70% then our binomial
30				probability distribution will be as follows:
30.87				The binomial probability function is given by:
64200				P (x) = n ∏ x ( 1-∏ ) n-x
Edison, NJ Metropolitan Division				X
50				Where in our case n = 5 which is the number of
31.12				employment per month, x = 0,1,2,3,4,5) which are
64720				the number of outcomes per month, ∏ = 0.7
New York-White Plains-Wayne, NY-NJ Metropolitan				which is the probability that the employment level
Division				will increase by 5% from 2006 to 2016.
6920				Our binomial distribution is as follows after
37.7				calculations:x
78410				P(x)
Nassau-Suffolk, NY Metropolitan Division				0
380				0.00243
37.28				1
77540				0.02835
New York-Northern New Jersey-Long Island,				2
NY-NJ-PA				0.1323
7390				3
37.71				0.3087
78450				4
New York-White Plains-Wayne, NY-NJ Metropolitan				0.36015
Division				5
6920				0.16807
37.7				If we are to draw a chart regarding the binomial
78410				probability distribution then our chart will be as
Portland-Vancouver-Beaverton, OR-WA				follows:
200				The binomial probability distribution helps us
32.01				estimate the probability of an outcome, in this
66590				case we can be in a position to estimate the
Allentown-Bethlehem-Easton, PA-NJ				probability for example what is the probability that
30				the persons who are likely to be employed will be
30.87				greater than 2 individuals, more than 3 individuals
64200				or even less than one individuals, for this reason
Philadelphia, PA Metropolitan Division				therefore the probabilities can be calculated by
120				adding the probabilities of each outcome to come
25.47				up with the desired answer in question.
52970				Hypothesis testing:
Philadelphia-Camden-Wilmington, PA-NJ-DE-MD				We still consider our data from the fashion design
270				industry to analyse the data, in hypothesis testing
31				we will consider hypothesis test for the data and
64480				stating the null and alternative hypothesis, in this
Reading, PA				case therefore it is clear that we will have to use
270				the T table, Z table or even the F table on the
20.22				nature of the test and deepening on the
42050				hypothesis in question
Dallas-Plano-Irving, TX Metropolitan Division				Confidence interval:
550				90% confidence interval:
37.22				When we are constructing the confidence interval
77420				we consider the standard deviation, the mean and
Fort Worth-Arlington, TX Metropolitan Division				the value from the T tables at 90% level of
40				measure: we lookup 10% at two tail from the T
14.42				table and the figure is 2.015048:
29980				Our confidence interval will take the following
Portland-Vancouver-Beaverton, OR-WA				form:
200				P(x – st) ≤ (x + st) = 90%
32.01				Where X is the mean, S is the standard deviation
66590				and T is the value from the tables:
Seattle-Bellevue-Everett, WA Metropolitan Division				P(32.54 –(3.07 X 2.015) ≤ X ≤ (32.54 +
160				(3.07 X 2.015) = 90%
27.03				P(26.35395) ≤ X ≤ (38.72605) = 90%
56210				This confidence interval states that at 90%
Seattle-Tacoma-Bellevue, WA				confidence interval the mean will range from 26.35
160				to 38.72 where they are the lower and upper
27.03				bound respectively. This also means that we are
56210				90% confident that the mean ranges from 26.35
Minneapolis-St. Paul-Bloomington, MN-WI				to 38.72
90				95% confidence interval:
27.64				When we lookup 5% at two tail t test then the
57490				value is 0.726687, therefore our confidence
Bridgeport-Stamford-Norwalk, CT				interval will be as follows:
110				P(32.54 –(3.07 X 0.726687) ≤ (32.54 + (3.07
25.68				X 0.726687) = 95%
53410				P(30.30907091) ≤ X ≤ (34.77093) = 95%
Mean, standard deviation and median:				This confidence interval states that at 95%
When we use ungrouped data to analyse the				confidence interval the mean will range from 30.30
mean and the median of the data our results are				to 34.77 where they are the lower and upper
as follows:total				bound respectively. This also means that we are
31500				95% confident that the mean ranges from 30.30
903.66				to 34.77.
1879590mean				From the measure of confidence interval it is
1050				clear that when we consider a larger confidence
30.122				interval then it is clear that the lower is the range
62653standard deviation				of the interval as compared to when we use a
2147.812038				lower confidence interval.
5.384997295				Linear regression:
11203.3099				We will perform the regression model on the
MIN				employment level and the hourly wage rate, we
30				will assume that the higher the level of
14.42				employment then the higher is the wage rate,
29980				therefore we will assume that the wage rate
MAX				dependent on the rate of employment, in this
7390				case therefore our dependent variable will be
37.71				wage rate and the independent variable will be
78450				employment level:
RANGE				After estimation our:
7360				B = 0.0005673
23.29				α = 31.391809
48470				Therefore our estimated model will take the
The mean hourly wage is 30.12 dollars, the range				following form below:
is 23.29 and our standard deviation is equal to				Y = 31.39 + 0.0005673 X
5.38, these are measures of central tendencies of				We can define this model as follows, if we hold all
data, the mean gives us an estimate of the				other factors constant and the level of
hourly wage rate in the fashion industry and the				employment is zero then the level of wage rate
standard deviation give us the measure of				will be 31.39. if we hold all other factors constant
deviations from the mean of the different wages				and increase the level of employment by one unit
paid by different states.				then the wage rate level per hour will increase by
Grouped data:				0.0005673 units.
When we group the data into 6 classes and				For this reason therefore it is clear that our earlier
considering the class interval to be two then we				stated objective has been achieved, this is in
will be in a position to obtain our frequency and				reference to the objective that an increase in
therefore construct a histogram, after grouping				employment will raise the wage rate level.
our data the results are as				Correlation:
follows:classfrequencycummulative				When we undertake the calculation of the
frequencypercentage				Pearson correlation coefficient then our correlation
10.50 TO 15.50				after calculation is equal to 0.8366, from the figure
1				of the coefficient it is clear that we have positive
1				correlation between the two data, we also have a
3%				moderately strong relation and this is obtained by
15.51 TO 20.50				the fact that the correlation coefficient is close to
2				1, we therefore can conclude that there is a
3				strong positive correlation between employment
7%				and wage rate per hour.
20.51 TO 25.50				Summary:
4				From our statistical analysis that we have
7				performed on the fashion and design industry it is
13%				clear that the industry provides employment to a
25.51 TO 30.50				large number of individuals in the United States, in
8				our selected states which are 6 in number the
15				industry employs over 12,000 individuals according
27%				to the 2006 statistics.
30.51 TO 35.50				According to the bureau of labour in the United
9				States the growth rate of this industry is
24				expected to grow by 2016 where its
30%				employment rate will increase by 5%, when
35.51 TO 40.50				calculating using the percentage given then it is
6				clear that by 2016 the employment level of the
30				industry in our selected state will increase from
20%				19,000.
30				When we perform a linear regression estimation
100%				of the data and consider that the wage rate is
Our histogram will be as follows:				dependent on the employment level then it is
This histogram shows that there is a high				clear that the employment level positively affect
possibility that the wage rate will be between				the wage rate, this is to say that the higher the
30.51 to 35.50, to be precise the probability that				employment level then the higher is the wage
the wage rage will be at this level is 0.5 or 50%				rate. Further we found a strong correlation
probability.				coefficient between wage rate and employment.
Also our or give will be as follows:				Finally we conclude by saying that there is a need
The orgive represents the cumulative frequency				to use a larger sample size in order to get a
data and shows the trend of the cumulative				clearer picture of the fashion and design industry,
frequency to the 100% level.				a large data sample will allow us to overcome
The stem and leaf:				biasness in statistical analysis, samples are
A stem and leaf diagram displays the trends in				expected to be a representative of the entire
data and also gives us an overview of the nature				population, for this reason therefore there is need
of the data, whether skewed or normal				to select a larger sample size and compare the
distribution. Below is the stem and leaf diagram:				results.

DAN

79130524 Employees In The Fashion Designers Industry