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商科统计代写 |人口统计代写 | 数据分析

2020-03-20 21:15 星期五 所属: 数据分析 浏览:18

商科统计代写 The population we want to compare are performance in exams of students whose race/ethnicity are grouped B/C/D.

 

Part 1

Introduction

The population we want to compare are performance in exams of students whose race/ethnicity are grouped B/C/D.

Complete data can download from https://www.kaggle.com/spscientist/students-performance-in-exams. This dataset includes scores from three exams and a variety of personal, social, and economic factors that have interaction effects upon them. There are three quantitative variables and five categorical variables. Group B has 190 records, group C has 329 records, group D has 262 records.商科统计代写

Qualitative variables we observed were “gender” and “parental level of education”. “gender” male means students are male, “gender” female means students are female. “parental level of education” gives the level of education of students’ parents.

Quantitative variables we observed were “math score” / “reading score”/ “writing score” which are relative exam scores.商科统计代写

Part 2

Sample and collect data

We use simple random sampling without replacement to get the subset of the complete dataset.

Step1: add a column as id number series for each group B/C/D.

Step2: use Sampling tool that’s part of the Data Analysis command, set id number column as the input range, then remove the replicate items, make sure the sample size is 30.商科统计代写

Frequency Tables and Pie Charts

For each qualitative variable, make a frequency table and a pie chart.

1) gender

The pie chart above show the gender of the 30 students exam records sampled from race group B/C/D. 商科统计代写we can see that the number of female students are equal with the number of male students in group B samples, the number of female students are less than the number of male students in group C and group D samples.

2) parental level of education

The pie charts above show parental level of education of the 30 samples from race group B/C/D. we can see that student’s parental level of education in group D has the highest proportion of bachelor’s degree. High school proportions are same in group B and group C.

Part 3

Box Plot

The boxplots above to the left shows the math scores of the 30 students sampled from race group B, group C, and group D. 商科统计代写The boxplots show that group C has the least variation in math scores, while group D has the largest variation in math scores. Also, we can see that the medium math score of group D is higher than that of group B and group C.

The boxplots above in the center show the reading scores of the 30 students sampled from race group B, group C and group D. the boxplots show that group B has the largest variation. Once again, the median reading score of group D is higher than that of group B and group C.

The boxplots above in the right show the writing scores of the 30 students sampled from race group B, group C and group D. the boxplots show that the group B has the smallest variation. Once again, the median writing score of group D is higher than that of group B and group C.

Recall that the parental level of education in subgroup C have the highest proportion in bachelor’s degree, maybe students who parents with higher education are more likely to get higher score in their own exams.

Part 4

Inferential Analysis

The table below shows the mean, standard deviation, and the mean’s margin of error for each quantitative variables and population. 商科统计代写The margins of error are calculated using a normal distribution and a 95% confidence level.

 

population

groupB

groupC

groupD

math scores

mean

60.77

64.63

67.80

standard deviation

17.43

14.46

15.79

margin of error

6.24

5.17

5.65

reading scores

mean

63.87

68.33

69.03

standard deviation

18.14

15.10

17.18

margin of error

6.49

5.41

6.15

writing scores

mean

62.07

66.57

68.73

standard deviation

18.50

17.22

17.00

margin of error

6.62

6.16

6.08

The charts below show the means and confidence intervals for each quantitative variables and population. Assuming a normal distribution of sample means, 商科统计代写 there is a 95% probability that the true mean of a population lies within the confidence interval shown for it.

Part 5

Hypothesis Testing

1) Variation of reading scores in group B and group C.

It appears from the boxplot that the variation among the reading scores in group B is less than that of in group C. Also, 商科统计代写 the standard deviation of reading scores in group B sample is 15.10, while the standard deviation of reading scores in group C sample is 18.14.

To see whether this is a statistically significant finding at the 5% level of significance, an F-stat was performed.

We use the “F-test two sample for Variances” command in Data Analysis. then we get the following table:

F-Test Two-Sample for Variances

 

 

 

 

 

Variable 1

Variable 2

Mean

63.87

68.33

Variance

329.22

228.16

Observations

30

30

df

29

29

F

1.44

 

P(F<=f) one-tail

0.16

 

F Critical one-tail

1.86

 

The result show p-value for test is 0.16, so we don’t have enough evidence to reject the null hypothesis that reading scores of group B and group C’s variances are same at the 5% level of significance.

2) mean of reading scores in group B and group C.

Further, the mean value of reading scores in group B and group C respectively are 63.87 and 68.33. we want to see whether this is a statistically significant finding at 5% level of significance. Then a two-sample t-test is conducted.

By using the “t-Test: Two-Sample Assuming Equal Variances” command in Data Analysis, we can get the following result:

t-Test: Two-Sample Assuming Equal Variances

 

 

 

 

Variable 1

Variable 2

Mean

63.87

68.33

Variance

329.22

228.16

Observations

30

30

Pooled Variance

278.69

 

Hypothesized Mean Difference

0

 

df

58

 

t Stat

-1.04

 

P(T<=t) one-tail

0.15

 

t Critical one-tail

1.67

 

P(T<=t) two-tail

0.30

 

t Critical two-tail

2.00

 

The results above show that the p-value one tail for testing is 0.15, also, we don’t have enough evidence to reject the null hypothesis that there is no significant difference between the mean reading score in group B and the mean reading score in group C.

3) Mean math score of group A and group C

Same as 1) and 2), 商科统计代写 we first conduct the variance testing using F-test, then using T-testing to test the mean of two sample.

The testing result are listed as below:

F-Test Two-Sample for Variances

 

 

 

 

 

Variable 1

Variable 2

Mean

60.77

67.80

Variance

303.98

249.20

Observations

30

30

df

29

29

F

1.22

 

P(F<=f) one-tail

0.30

 

F Critical one-tail

1.86

 

 

 

 

 

 

 

t-Test: Two-Sample Assuming Equal Variances

 

 

 

 

Variable 1

Variable 2

Mean

60.77

67.80

Variance

303.98

249.20

Observations

30

30

Pooled Variance

276.59

 

Hypothesized Mean Difference

0

 

df

58

 

t Stat

-1.64

 

P(T<=t) one-tail

0.05

 

t Critical one-tail

1.67

 

P(T<=t) two-tail

0.11

 

t Critical two-tail

2.00

 

The results shows that at the significance level 0.05, the mean math score of group B are equal with the mean score of group D.

 

 

 

 

Appendix-Sample Data

Group B

gender

race/ethnicity

parental level of education

lunch

test preparation course

math score

reading score

writing score

male

group B

some college

free/reduced

none

40

43

39

female

group B

some college

free/reduced

completed

65

75

70

male

group B

associate’s degree

standard

none

65

54

57

male

group B

some high school

standard

none

67

64

61

female

group B

associate’s degree

standard

none

47

49

50

female

group B

some college

standard

none

79

86

92

male

group B

high school

standard

completed

60

44

47

female

group B

high school

standard

completed

68

83

78

male

group B

some high school

standard

completed

61

56

56

male

group B

associate’s degree

standard

none

87

85

73

female

group B

some high school

standard

none

37

46

46

male

group B

associate’s degree

free/reduced

none

67

62

60

female

group B

some college

free/reduced

none

61

68

66

female

group B

bachelor’s degree

standard

none

61

72

70

female

group B

associate’s degree

standard

none

80

86

83

female

group B

high school

free/reduced

none

50

67

63

male

group B

associate’s degree

standard

completed

65

65

63

female

group B

associate’s degree

free/reduced

none

53

70

70

male

group B

some college

standard

completed

71

75

70

male

group B

high school

free/reduced

none

30

24

15

female

group B

bachelor’s degree

standard

completed

65

81

81

female

group B

some high school

free/reduced

completed

59

63

64

male

group B

high school

standard

completed

76

62

60

female

group B

high school

standard

completed

77

82

89

male

group B

associate’s degree

standard

completed

82

84

78

female

group B

high school

free/reduced

none

64

73

71

male

group B

high school

free/reduced

none

36

29

27

male

group B

high school

standard

none

82

82

80

male

group B

some college

free/reduced

completed

60

62

60

female

group B

high school

free/reduced

none

8

24

23

 

group C

gender

race/ethnicity

parental level of education

lunch

test preparation course

math score

reading score

writing score

female

group C

some college

free/reduced

none

76

83

88

male

group C

some high school

free/reduced

completed

53

37

40

female

group C

associate’s degree

standard

none

59

66

67

female

group C

some college

free/reduced

none

22

39

33

male

group C

some high school

free/reduced

completed

59

69

65

female

group C

some college

standard

completed

88

95

94

female

group C

some high school

standard

completed

85

92

93

male

group C

some high school

standard

none

51

52

44

male

group C

high school

standard

none

71

66

65

female

group C

high school

free/reduced

completed

67

79

84

female

group C

bachelor’s degree

standard

none

83

93

95

female

group C

some college

standard

completed

63

78

80

male

group C

some high school

free/reduced

none

69

71

65

male

group C

high school

standard

none

61

56

55

female

group C

some college

standard

none

84

87

91

male

group C

some college

free/reduced

none

68

68

61

female

group C

high school

free/reduced

none

36

53

43

male

group C

associate’s degree

standard

completed

51

60

58

male

group C

high school

standard

completed

75

69

68

female

group C

some college

free/reduced

completed

63

73

71

male

group C

some college

standard

none

53

39

37

female

group C

high school

standard

none

81

84

82

male

group C

high school

standard

none

62

67

58

female

group C

high school

standard

completed

60

64

74

male

group C

some high school

standard

none

64

58

51

male

group C

bachelor’s degree

standard

completed

63

64

66

male

group C

high school

free/reduced

none

54

72

59

female

group C

bachelor’s degree

free/reduced

none

67

75

72

male

group C

bachelor’s degree

free/reduced

completed

70

75

74

male

group C

high school

standard

none

81

66

64

 

Group D

mso-border-left-alt:none;border-right:1.0000pt solid windowtext;mso-border-right-alt:0.5000pt solid windowtext;

gender

race/ethnicity

parental level of education

lunch

test preparation course

math score

reading score

writing score

male

group D

associate’s degree

standard

none

40

52

43

male

group D

bachelor’s degree

free/reduced

completed

74

71

80

female

group D

some college

standard

none

69

74

74

male

group D

high school

standard

none

88

78

75

male

group D

some high school

free/reduced

none

45

37

37

male

group D

bachelor’s degree

free/reduced

completed

74

79

75

male

group D

some high school

free/reduced

completed

80

79

79

male

group D

some college

standard

none

76

64

66

male

group D

associate’s degree

standard

none

80

75

77

female

group D

associate’s degree

standard

completed

88

92

95

female

group D

bachelor’s degree

standard

none

59

70

73

female

group D

some college

standard

none

77

68

77

male

group D

associate’s degree

standard

none

71

66

60

female

group D

bachelor’s degree

standard

none

79

89

89

female

group D

associate’s degree

free/reduced

none

52

59

56

male

group D

some high school

free/reduced

none

62

49

52

female

group D

some college

standard

none

74

89

84

male

group D

high school

free/reduced

none

60

57

51

male

group D

high school

standard

none

46

34

36

male

group D

high school

standard

none

89

87

79

female

group D

high school

free/reduced

none

73

92

84

female

group D

some high school

free/reduced

completed

40

65

64

male

group D

bachelor’s degree

free/reduced

completed

39

42

38

male

group D

some high school

standard

completed

88

74

75

female

group D

bachelor’s degree

free/reduced

completed

93

100

100

male

group D

bachelor’s degree

free/reduced

none

50

42

48

male

group D

high school

free/reduced

none

74

70

69

female

group D

high school

free/reduced

completed

65

61

71

female

group D

some college

standard

none

62

70

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