Confidence Interval
The quantitative variable of interest chosen for this discussion is the continuous variable “Highest Year of school completed”. This variable has been calculated, measured and analyzed by using the SPSS as statistical toll to see the trends and the differences when the confidence interval changes from 90% to 95%, as well as the size of sample change (100 and 400).
Random sample of 100
The confidence interval of the 100 sample of the total population (2538) responded to this data at:
The mean of 100 sample of this variable at 90% of confidence interval is 13.72 and at the 95% is 13.47.
The standard deviation of this variable at 90% confidence interval is 3.150, and at 95% of confidence interval is 3.239.
Descriptive Statistics 


N 
Minimum 
Maximum 
Mean 
Std. Deviation 
HIGHEST YEAR OF SCHOOL COMPLETED 
100 
6 
20 
13.72 
2.854 
Valid N (listwise) 
100 




Figure 1: Random sample of 100
Descriptives 


Statistic 
Std. Error 

HIGHEST YEAR OF SCHOOL COMPLETED 
Mean 
13.72 
.315 

90% Confidence Interval for Mean 
Lower Bound 
13.20 


Upper Bound 
14.24 


5% Trimmed Mean 
13.79 


Median 
14.00 


Variance 
9.921 


Std. Deviation 
3.150 


Minimum 
2 


Maximum 
20 


Range 
18 


Interquartile Range 
4 


Skewness 
.415 
.241 

Kurtosis 
1.376 
.478 
Figure 2: 90% confidence interval of 100 random sample.
Descriptives 


Statistic 
Std. Error 

HIGHEST YEAR OF SCHOOL COMPLETED 
Mean 
13.47 
.324 

95% Confidence Interval for Mean 
Lower Bound 
12.83 


Upper Bound 
14.11 


5% Trimmed Mean 
13.56 


Median 
13.00 


Variance 
10.494 


Std. Deviation 
3.239 


Minimum 
3 


Maximum 
20 


Range 
17 


Interquartile Range 
4 


Skewness 
.351 
.241 

Kurtosis 
.602 
.478 
Figure 3: 95% confidence interval of 100 random sample.
Random sample of 400
The confidence interval of the 400 sample of the total population (2538) responded to this data at:
The mean of 400 sample of this variable at both 90% and 95% of confidence intervals is 13.83. The standard deviation of this variable at 90% and 95% of confidence intervals is 2.983.
Descriptive Statistics 


N 
Minimum 
Maximum 
Mean 
Std. Deviation 
HIGHEST YEAR OF SCHOOL COMPLETED 
400 
0 
20 
13.62 
3.076 
Valid N (listwise) 
400 




Figure 4: Random sample of 400
Descriptives 


Statistic 
Std. Error 

HIGHEST YEAR OF SCHOOL COMPLETED 
Mean 
13.83 
.149 

95% Confidence Interval for Mean 
Lower Bound 
13.54 


Upper Bound 
14.12 


5% Trimmed Mean 
13.86 


Median 
14.00 


Variance 
8.898 


Std. Deviation 
2.983 


Minimum 
0 


Maximum 
20 


Range 
20 


Interquartile Range 
4 


Skewness 
.382 
.122 

Kurtosis 
1.854 
.243 
Figure 5: 95% confidence interval of 400 random sample.
Descriptives 


Statistic 
Std. Error 

HIGHEST YEAR OF SCHOOL COMPLETED 
Mean 
13.83 
.149 

90% Confidence Interval for Mean 
Lower Bound 
13.58 


Upper Bound 
14.08 


5% Trimmed Mean 
13.86 


Median 
14.00 


Variance 
8.898 


Std. Deviation 
2.983 


Minimum 
0 


Maximum 
20 


Range 
20 


Interquartile Range 
4 


Skewness 
.382 
.122 

Kurtosis 
1.854 
.243 
Figure 6: 90% confidence interval of 400 random sample.
Based on the descriptive statistics of the chosen variable for this discussion, and all figures presented in this page, the confidence interval knows some very minimal changes and is impacted by the size of the sample and the confidence interval levels (90% and 95%). Also I noticed that the confidence interval at 95% for upper bound 14.11 remained the same. When the random sample increased from 100 to 400, the standard deviation decreased from 3.150 at 90% and 3.239 at 95% to 2.983.
Regarding the statement, “Confidence intervals are underutilized”, majority of student or professionals do not take into account the sample size of the population or they misuse it. Sample size estimation is based on scientific calculation and confidence level to obtain or achieve a certain level of confidence and accuracy of the data that represents the reality or describe the studied subject in a concrete manner. The implications that may occur when not using the confidence intervals will be related to validity and reliability of the research and data presented, witch may raise lot of questions of the integrity of the researcher.
Note: I am attaching the response for this discussion in word document in case the table are not shown in this discussion space.
Reference
FrankfortNachmias, C., & LeonGuerrero, A. (2011). Social statistics for a diverse society (6^{th }ed). Thousand Oaks, CA: Sage Publications.
Wagner, W. E. (2016). Using IBM SPSS Statistics for research methods and social science statistics (6^{th} ed.). Thousand Oaks, CA: Sage Publications.
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