Essentials of Statistics and Economics Assignment Help

Essentials of Statistics and Economics Assignment Help

Essentials of Statistics and Economics Assignment Help

Question 1

Visual presentation of the prices based on product from different brands

Price of Calvin Klein

Price of Zara

Price of Tommy Hilfiger

Price of Ralph Lauren

94.27

47.53

60.73

63.77

70.71

48.87

87.92

97.55

60.48

58.19

47.07

64.47

61.83

32.64

96.78

149.02

73.78

54.35

83.47

29.53

82.79

51.75

92.30

95.28

65.26

75.09

35.89

131.19

48.48

61.67

118.92

54.59

78.00

31.28

98.56

100.66

81.44

42.92

72.89

111.94

128.17

72.02

49.06

32.78

31.00

28.04

14.38

80.25

37.42

60.34

79.39

89.56

64.86

59.32

130.20

115.84

63.02

34.98

41.18

22.08

84.65

56.49

47.57

38.35

84.74

25.07

29.02

41.41

86.82

36.22

44.24

62.18

50.59

70.48

87.10

77.11

41.17

39.91

60.49

45.88

57.74

46.55

72.93

60.77

29.09

48.50

98.93

41.05

63.03

52.36

52.82

94.84

60.27

66.86

123.02

89.81

56.75

38.36

15.42

74.94

44.24

51.88

56.38

73.80

109.63

47.16

103.36

60.55

101.15

54.65

105.25

44.30

100.12

66.34

86.78

42.48

75.55

73.45

124.03

59.07

Charts

Charts

One of the fundamental aspects in representing the data output on prices is through distribution. The price distribution arises because the rates will not yield the same at every time due to various macro and micro economic factors.  Therefore, there exist a scattering of values around central tendency. The location, shape and variability of the distributions can be analysed using the following tools. (Freedman, 2010)

Location – Mean & median; Spread – Variance, Standard deviation and range and Shape – Skewness and Kurtosis

The descriptive statistics of prices

 

Calvin Klein

 

 

 

 

Location

Mean

69.56889

 

Median

65.05888

Spread

Standard Deviation

23.37837

 

Sample Variance

546.5483

 

Range

99.08802

Shape

Kurtosis

0.111549

 

Skewness

0.401199

 

Minimum

29.08674

 

Maximum

128.1748

 

Count

30

 

Zara

 

 

 

 

Location

Mean

51.10847

 

Median

51.8144

Spread

Standard Deviation

13.86985

 

Sample Variance

192.3726

 

Range

50.02136

Shape

Kurtosis

-0.77666

 

Skewness

-0.05338

 

Minimum

25.06978

 

Maximum

75.09114

 

Count

30

 

Tommy Hilfiger

 

 

 

 

Location

Mean

73.86924

 

Median

76.16283

Spread

Standard Deviation

32.29041

 

Sample Variance

1042.671

 

Range

115.8186

Shape

Kurtosis

-0.86718

 

Skewness

-0.06482

 

Minimum

14.38371

 

Maximum

130.2023

 

Count

30

 

Ralph Lauren

 

 

 

 

Location

Mean

71.50168

 

Median

64.12269

Spread

Standard Deviation

31.26372

 

Sample Variance

977.4204

 

Range

126.9439

Shape

Kurtosis

-0.07787

 

Skewness

0.600018

 

Minimum

22.07529

 

Maximum

149.0192

 

Count

30

From the above descriptive analysis it is noted that the mean and median value of Calvin Klein is different, the mean states the average of the distribution whereas the median states the 50 percentile of the data or the mid value. However, it is noted that mean and median of Zara is almost same at 51, however Tommy Hilfiger and Ralph Lauren is also have a difference between the mean and median

Essentials of Statistics and Economics Assignment Help

While measuring the spread of the data, the standard deviation of Calvin Klein, Tommy Hilfiger and Ralph Lauren has highest value, this shows that the deviation of the values from the mean is huge. Therefore a large standard deviation means the observed value has a huge difference when compared with mean. Therefore the goal should be less standard deviation which is noted in Zara. Therefore, it can be stated that the mean value of Zara has more meaningful information . (Triola, 2014)

In order to analyse the shape of the data, skewness and kurtosis is applied, skewness will state the symmetry of the data. A data to be normally distributed should possess the value of skewness as 0. Similarly Kurtosis is used to measure the combined size of two tails of information, for a data to be normally distributed should have value equal to 3. In the descriptive analysis it is noted that Zara and Tommy Hilfiger has a skewness value almost 0, whereas Calvin Klein and Ralph Lauren have values more than 0, therefore these two products are asymmetrical and the prices may not have normal distribution.

Question 2

Visual representation

Visual representation

 

Business Style

 

 

 

 

Location

Mean

89.14395

 

Median

87.36749

Spread

Standard Deviation

22.28638

 

Sample Variance

496.6829

 

Range

73.71693

Shape

Kurtosis

-0.94622

 

Skewness

0.274778

 

Minimum

56.48535

 

Maximum

130.2023

 

Count

30

 

Sports style

 

 

 

 

Location

Mean

64.06367

 

Median

61.19693

Spread

Standard Deviation

15.32209

 

Sample Variance

234.7665

 

Range

62.71523

Shape

Kurtosis

-0.6026

 

Skewness

0.34497

 

Minimum

36.21763

 

Maximum

98.93286

 

Count

30

 

Casual style

 

 

 

 

Location

Mean

41.33898

 

Median

41.17424

Spread

Standard Deviation

13.02517

 

Sample Variance

169.655

 

Range

50.87537

Shape

Kurtosis

-0.36824

 

Skewness

-0.11966

 

Minimum

14.38371

 

Maximum

65.25908

 

Count

30

From the above descriptive analysis it is noted that the mean and median value of Business style and Sports style wears are different, the mean states the average of the distribution whereas the median states the 50 percentile of the data or the mid value. However, it is noted that mean and median of Casual style wear is almost same at 41. Therefore the mean and median is closely related for Casual style wear. (Boslaugh, 2012)

While measuring the spread of the data, the standard deviation of Business style has highest value with 22.28, this shows that the deviation of the values from the mean is huge. Therefore a large standard deviation means the observed value has a huge difference when compared with mean. Therefore the goal should be less standard deviation which is noted in Sports style and Casual style with SD of 15.32 and 13.02 respectively. Therefore, it can be stated that the mean value of Business style and Casual style has more meaningful information .

In order to analyse the shape of the data, skewness and kurtosis is applied, skewness will state the symmetry of the data. A data to be normally distributed should possess the value of skewness as 0. Similarly Kurtosis is used to measure the combined size of two tails of information, for a data to be normally distributed should have value equal to 3. In the descriptive analysis it is noted that Casual style has a skewness value almost 0, whereas Business style and Sports style have values more than 0, therefore these two style are asymmetrical and the prices may not have normal distribution.

Question 3

Zara business

Zara sports

Zara casual

58.19

54.35

47.53

75.09

51.75

48.87

72.02

61.67

32.64

60.34

42.92

31.28

59.32

36.22

28.04

56.49

48.50

34.98

70.48

52.36

25.07

66.86

51.88

39.91

66.34

47.16

46.55

73.45

54.65

38.36

Essentials of Statistics and Economics Assignment Help

 

Zara business style

 

 

 

 

Location

Mean

65.85872

 

Median

66.60369

Spread

Standard Deviation

6.859775

 

Sample Variance

47.05652

 

Range

18.60579

Shape

Kurtosis

-1.73364

 

Skewness

-0.07044

 

Minimum

56.48535

 

Maximum

75.09114

 

Count

10

 

Zara sports style

 

 

 

 

Location

Mean

50.14484

 

Median

51.8144

Spread

Standard Deviation

6.984534

 

Sample Variance

48.78372

 

Range

25.45067

Shape

Kurtosis

1.056389

 

Skewness

-0.56811

 

Minimum

36.21763

 

Maximum

61.6683

 

Count

10

 

Zara casual style

 

 

 

 

Location

Mean

37.32185

 

Median

36.6685

Spread

Standard Deviation

8.370247

 

Sample Variance

70.06104

 

Range

23.8008

Shape

Kurtosis

-1.32792

 

Skewness

0.102239

 

Minimum

25.06978

 

Maximum

48.87058

 

Count

10

From the above descriptive analysis it is noted that the mean and median value of all style of products of Zara looks same, the mean states the average of the distribution whereas the median states the 50 percentile of the data or the mid value. However, it is noted that mean and median of all products of Zara  is almost same.

The goal should be less standard deviation which is noted in Business style, Sports style and Casual style of Zara products are less. Therefore, it can be stated that the mean value of all products  are closely related to the mean value.

In order to analyse the shape of the data, skewness and kurtosis is applied, skewness will state the symmetry of the data. A data to be normally distributed should possess the value of skewness as 0. Similarly Kurtosis is used to measure the combined size of two tails of information, for a data to be normally distributed should have value equal to 3. In the descriptive analysis it is noted that business style has a skewness value almost 0, whereas sports style and Sports style have values more than 0, therefore these two style are asymmetrical and the prices may not have normal distribution. (Witte, 2010)

Question 4

A t-test is one of the statistical test which helps the researcher to determine whether the two set of data is significantly different from each other. A t test is one of the commonly implemented test analysis, which will follow the steps of the normal distribution. It should be noted that when the scaling term is unknown and it is replaced by an estimate which is available on the data then we can follow students t-test. (Sincich, 2012)

The first step is to formulate the hypothesis, the null hypothesis will state that there mean difference is the same or to put it in other words, there is no significant difference between the variables. The alternate hypothesis will be stated as there is a significant difference among the variables. The interpretation of the data can be stated if the test statistic value is greater than the significance value then null hypothesis is rejected and alternate hypothesis is accepted. (Freedman, 2010)

In the given problem, the objective is to test if there is a significant difference in average prices across these two gender targets. Therefore the following hypothesis is framed.

Null hypothesis: There is no significant difference between average prices and gender

Alternate hypothesis:There is a significant difference between average prices and gender

t-Test: Two-Sample Assuming Unequal Variances

 

 

 

 

 

 

 

 

Price

Gender

 

Mean

66.51207

1.5

 

Variance

754.4582

0.252101

 

Observations

120

120

 

Hypothesized Mean Difference

0

 

 

df

119

 

 

t Stat

25.92355

 

 

P(T<=t) one-tail

0.004

 

 

t Critical one-tail

1.657759

 

 

P(T<=t) two-tail

0.008

 

 

t Critical two-tail

1.9801

 

 

From the above t-test analysis it can be noted that mean value of price is 66.51 and the gender is 1.5, the variance of prices are high when compared with the gender.

It is further noted that t statistic is 25.92 whereas the p value is 0.004, this shows that the mean of values between price changes and gender are same. Therefore, null hypothesis is accepted. Hence it is stated that there is no significant difference between average prices and gender.

Question 5

A t-test is one of the statistical test which helps the researcher to determine whether the two set of data is significantly different from each other. A t test is one of the commonly implemented test analysis, which will follow the steps of the normal distribution. It should be noted that when the scaling term is unknown and it is replaced by an estimate which is available on the data then we can follow students t-test.

The first step is to formulate the hypothesis, the null hypothesis will state that there mean difference is the same or to put it in other words, there is no significant difference between the variables. The alternate hypothesis will be stated as there is a significant difference among the variables. The interpretation of the data can be stated if the test statistic value is greater than the significance value then null hypothesis is rejected and alternate hypothesis is accepted.

In the given problem, the objective is to test if there is a significant difference in average prices across brands. Therefore the following hypothesis is framed.

Null hypothesis:There is no significant difference between average prices and brands

Alternate hypothesis:There is a significant difference between average prices and brands

t-Test: Two-Sample Assuming Unequal Variances

 

 

 

 

 

 

Price

Brands

Mean

66.27881803

2.512605042

Variance

754.2678226

1.25195841

Observations

119

119

Hypothesized Mean Difference

0

 

df

118

 

t Stat

25.30703038

 

P(T<=t) one-tail

0.008

 

t Critical one-tail

1.657869523

 

P(T<=t) two-tail

0.001

 

t Critical two-tail

1.980272226

 

From the above t-test analysis it can be noted that mean value of price is 66.27 and the brands is 1.5, the variance of prices are high when compared with the brands.

It is further noted that t statistic is 25.30 whereas the p value is 0.008, this shows that the mean of values between price changes and brands are same. Therefore, null hypothesis is accepted. Hence it is stated that there is no significant difference between average prices and brands.

Question 6

A t-test is one of the statistical test which helps the researcher to determine whether the two set of data is significantly different from each other. A t test is one of the commonly implemented test analysis, which will follow the steps of the normal distribution. It should be noted that when the scaling term is unknown and it is replaced by an estimate which is available on the data then we can follow students t-test.

The first step is to formulate the hypothesis, the null hypothesis will state that there mean difference is the same or to put it in other words, there is no significant difference between the variables. The alternate hypothesis will be stated as there is a significant difference among the variables. The interpretation of the data can be stated if the test statistic value is greater than the significance value then null hypothesis is rejected and alternate hypothesis is accepted. (Freedman, 2010)

In the given problem, the objective is to test if there is a significant difference in average prices across styles. Therefore the following hypothesis is framed.

Null hypothesis: There is no significant difference between average prices and styles

Alternate hypothesis:There is a significant difference between average prices and styles

t-Test: Two-Sample Assuming Unequal Variances

 

 

 

 

 

 

Prices

Styles

Mean

66.27881803

2.008403361

Variance

754.2678226

0.66942031

Observations

119

119

Hypothesized Mean Difference

0

 

df

118

 

t Stat

25.51697319

 

P(T<=t) one-tail

0.003

 

t Critical one-tail

1.657869523

 

P(T<=t) two-tail

0.007

 

t Critical two-tail

1.980272226

 

From the above t-test analysis it can be noted that mean value of price is 66.27 and the styles is 2.0, the variance of prices are high when compared with the styles.

It is further noted that t statistic is 25.5 whereas the p value is 0.003, this shows that the mean of values between price changes and styles are same. Therefore, null hypothesis is accepted. Hence it is stated that there is no significant difference between average prices and styles.

Question 7

A t-test is one of the statistical test which helps the researcher to determine whether the two set of data is significantly different from each other. A t test is one of the commonly implemented test analysis, which will follow the steps of the normal distribution. It should be noted that when the scaling term is unknown and it is replaced by an estimate which is available on the data then we can follow students t-test.

The first step is to formulate the hypothesis, the null hypothesis will state that there mean difference is the same or to put it in other words, there is no significant difference between the variables. The alternate hypothesis will be stated as there is a significant difference among the variables. The interpretation of the data can be stated if the test statistic value is greater than the significance value then null hypothesis is rejected and alternate hypothesis is accepted.

In the given problem, the objective is to test if there is a significant difference in Zara average prices across Zara styles. Therefore the following hypothesis is framed.

Null hypothesis:There is no significant difference between Zara average prices and Zara styles

Alternate hypothesis:There is a significant difference between Zara average prices and Zara styles

Zara prices and styles can be grouped as follows

PRICE

STYLE

47.53

3

48.87

3

58.19

1

32.64

3

54.35

2

51.75

2

75.09

1

61.67

2

31.28

3

42.92

2

72.02

1

28.04

3

60.34

1

59.32

1

34.98

3

56.49

1

25.07

3

36.22

2

70.48

1

39.91

3

46.55

3

48.50

2

52.36

2

66.86

1

38.36

3

51.88

2

47.16

2

54.65

2

66.34

1

73.45

1

t-Test: Two-Sample Assuming Unequal Variances

 

 

 

 

 

 

Zara prices

Zara styles

Mean

51.23195651

1.965517241

Variance

198.7692613

0.677339901

Observations

29

29

Hypothesized Mean Difference

0

 

df

28

 

t Stat

18.78610969

 

P(T<=t) one-tail

0.0014

 

t Critical one-tail

1.701130908

 

P(T<=t) two-tail

0.002

 

t Critical two-tail

2.048407115

 

From the above t-test analysis it can be noted that mean value of Zara average price is 51.23 and the styles of Zara is 1.96, the variance of prices are high when compared with the styles.

It is further noted that t statistic is 18.8 whereas the p value is 0.001, this shows that the mean of values between price changes and styles are same. Therefore, null hypothesis is accepted. Hence it is stated that there is no significant difference between Zara average prices and Zara styles.

References

Boslaugh, Sarah (2012). Statistics in a Nutshell. Cengage Publishing

Freedman, David (2010). Statistics. 4th Edition. Cengage Publishing

Sincich, T. Terry (2012). Statistics. 12th Edition.

Triola (2014). Essentials of Statistics. 5th Edition. McGraw Hill

Witte, S. Robert. (2010). Statistics. 5th Edition. McGraw Hill