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/studentsperformanceinexams. 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 Fstat was performed.
We use the “Ftest two sample for Variances” command in Data Analysis. then we get the following table:
FTest TwoSample 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) onetail 
0.16 

F Critical onetail 
1.86 

The result show pvalue 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 twosample ttest is conducted.
By using the “tTest: TwoSample Assuming Equal Variances” command in Data Analysis, we can get the following result:
tTest: TwoSample 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) onetail 
0.15 

t Critical onetail 
1.67 

P(T<=t) twotail 
0.30 

t Critical twotail 
2.00 

The results above show that the pvalue 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 Ftest, then using Ttesting to test the mean of two sample.
The testing result are listed as below:
FTest TwoSample 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) onetail 
0.30 

F Critical onetail 
1.86 







tTest: TwoSample 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) onetail 
0.05 

t Critical onetail 
1.67 

P(T<=t) twotail 
0.11 

t Critical twotail 
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.
AppendixSample 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
msoborderleftalt:none;borderright:1.0000pt solid windowtext;msoborderrightalt: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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