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

stats project代写
stats project代写

Part 1

Introduction                           stats project代写

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.

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.

Part 2

Sample and collect data                       stats project代写

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.

Frequency Tables and Pie Charts

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

1) gender

stats project代写
stats project代写

The pie chart above show the gender of the 30 students exam records sampled from race group B/C/D. 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                       stats project代写

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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

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The boxplots above to the left shows the math scores of the 30 students sampled from race group B, group C, and group D. 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                 stats project代写

The table below shows the mean, standard deviation, and the mean’s margin of error for each quantitative variables and population. 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, there is a 95% probability that the true mean of a population lies within the confidence interval shown for it.

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Part 5

Hypothesis Testing                     stats project代写

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, 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.                  stats project代写

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               stats project代写

Same as 1) and 2), 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                                  stats project代写

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                             stats project代写
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                                   stats project代写
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 72
female group D some college free/reduced completed 67 86 83

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

stats project代写
stats project代写

 

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