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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:

90% is 13.20 for the Lower Bound and 14.24 for the upper Bound (figure 2).
95% is 12.83 for the Lower Bound and 14.11 for the upper Bound (figure 3).

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:

90% is 13.58 for the Lower Bound and 14.08 for the upper Bound (figure 6).
95% is 13.54 for the Lower Bound and 14.11 for the upper Bound (figure 5).

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

Frankfort-Nachmias, C., & Leon-Guerrero, A. (2011). Social statistics for a diverse society (6^thed). 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.