Data Analysis Homework: Statistical Analysis and Hypothesis Testing

This data analysis assignment presents a comprehensive analysis of a dataset, encompassing various statistical methods and interpretations. Part A of the assignment focuses on calculating descriptive statistics, including mean, standard deviation, and the application of the normal distribution to assess individual data points. Part B delves into inferential statistics, calculating the mean and standard deviation of a sample, determining confidence intervals, and analyzing error margins at different confidence levels and sample sizes. This section includes the creation of a graph to visualize the data. Part C involves hypothesis testing using t-tests, performing paired two-sample tests for means, and two-sample tests assuming unequal and equal variances. The assignment provides detailed calculations, interpretations, and the application of statistical concepts to draw meaningful conclusions from the provided data.

Data Analysis

Contents
TASK...............................................................................................................................................3
PART A...........................................................................................................................................3
Part B...............................................................................................................................................4
10 values from gathered data..................................................................................................4
PART C............................................................................................................................................6

TASK
PART A
Sr.no Name Marks Mean
Standard
Deviation
Normal
Distribution
1 Andy 87.8 69.67142857 12.92311159 0.011540611
2 Ken 67.8 0.030548455
3 Jerry 66 0.029649452
4 Tom 76.6 0.026737778
5 Marry 61 0.024647559
6 Chris 88.2 0.011044949
7 Jain 60 0.023330497
8 Hary 54.4 0.015357053
9 Mike 72.8 0.029978947
10 Santi 73.2 0.029740896
11 John 51.2 0.011115085
12 Michel 51.4 0.011362336
13 Alex 80.8 0.021306684
14 Elden 84.2 0.016409345
15 Eve 75 0.028354675
16 Alena 76.5 0.026848131
17 Joy 77 0.026285139
18 Roy 78.5 0.024445464
19 Kenedy 77.2 0.02605234
20 Berry 85.6 0.014442735
21 Roswell 88.9 0.010204663
22 Rosy 66.8 0.030117744
23 Simmi 87.5 0.011919405
24 Jas 66.7 0.030065106
25 Bantai 80.5 0.021731048

26 Sanju 79.9 0.022568783
27 Thor 75.4 0.02798169
28 Melina 82.5 0.018860849
29 Amaz 83.6 0.017269977
30 Khalifa 84.8 0.01555803
B)
Part B
10 values from gathered data
Andy 87.8
Ken 67.8
Jerry 66
Tom 76.6
Marry 61
Berry 85.6
Roswell 88.9
Rosy 66.8
Simmi 87.5
Jas 66.7
A) Mean sample.
Mean 75.47

B) Standard deviation
Standard
deviation 11.0100005
C) 95% confidence interval for M
Mean 75.47
Standard
deviation 11.0100005
count 10
Square root 3.16227766
t score 2.262157163
Confidence 7.876079896
D) Error margins by using five confidence levels.
Margin
of error 4.815246713 80%
5.796812076 90%
1.573735785 85%
0.786689576 70%
3.06263236 75%
E) Graph
F) Different error margins at a 95% confidence level with different sample size

When n=30
2.045229642
When n=5000
1.960438647
PART C
Mean
population 69.67142857
Std_d 12.92311159
Sample
mean 75.47
Sample
Size 10
Significant
level 95%

In order to test the hypothesis t- test is performed
A)
t-Test: Paired Two Sample for
Means
Variab
le 1 Variable 2
Mean 43.24 41.29727008
Variance
2077.5
5 1610.18574
Observations 2 2
Pearson Correlation 1
Hypothesized Mean Difference 0
df 1
t Stat
0.5038
4
P(T<=t) one-tail
0.3514
4
t Critical one-tail
6.3137
5
P(T<=t) two-tail
0.7028
8
t Critical two-tail
12.706
2
b)
t-Test: Two-Sample Assuming Unequal Variances
Variable
1 Variable 2
Mean 74.7267 75.47
Variance 119.597
121.22011
11
Observations 30 10
Hypothesized Mean Difference 0
df 15
t Stat -0.1852
P(T<=t) one-tail 0.42777
t Critical one-tail 1.75305
P(T<=t) two-tail 0.85555
t Critical two-tail 2.13145

C)
t-Test: Two-Sample Assuming equal
Variances
Variable
1 Variable 2
Mean 74.7267 75.47
Variance 119.597 121.2201111
Observations 30 10
Hypothesized Mean
Difference 0
df 15
t Stat -0.6852
P(T<=t) one-tail 0.39777
t Critical one-tail 1.15305
P(T<=t) two-tail 0.85555
t Critical two-tail 2.13145