Brilliant Answer

Respond to one of the colleague’s posts and explain how you might see the implications differently.

Alexis

The mean age for the respondents is 48.62. Confidence intervals are an estimated range of values that is likely to include an unknown population parameter (Yale University, 1997). Sometimes, not all the time, these random intervals cover the true population parameter. The width of a confidence interval will be smaller when there is a larger sample size. The width of the confidence interval will be larger when the overall population has a larger standard deviation. Also, the width of the confidence interval will be larger when the confidence level is higher. Due to confidence intervals being underutilized, confidence intervals should be included whenever a sample statistic such as a mean is presented as an estimate of the population parameter. Also, confidence intervals should be provided in addition to statistical significance for the hypothesis test. The data results of family income in constant $ shows that the increase in the sample size decreases the confidence interval's width, which means there was a reduction in the margin of error. 

 

 

Statistics
AGE OF RESPONDENT
N	Valid	508
	Missing	2
Mean	48.62
Median	48.00
Mode	38a
Range	70
Minimum	19
Maximum	89

   

The data below is the sample size of 100 and the CI of 90 % and 95%

 

One-Sample Test
	Test Value = 100
	t	df	Sig. (2-tailed)	Mean Difference	95% Confidence Interval of the Difference
					Lower	Upper
FAMILY INCOME IN CONSTANT $	21.256	469	.000	27240.207	24722.01	29758.41

 

 

One-Sample Test
	Test Value = 100
	t	df	Sig. (2-tailed)	Mean Difference	90% Confidence Interval of the Difference
					Lower	Upper
FAMILY INCOME IN CONSTANT $	21.256	469	.000	27240.207	25128.15	29352.26

 

 

The data below is the sample size of 400 and the CI of 90 % and 95%

 

One-Sample Test
	Test Value = 400
	t	df	Sig. (2-tailed)	Mean Difference	95% Confidence Interval of the Difference
					Lower	Upper
FAMILY INCOME IN CONSTANT $	21.022	469	.000	26940.207	24422.01	29458.41

 

One-Sample Test
	Test Value = 400
	t	df	Sig. (2-tailed)	Mean Difference	90% Confidence Interval of the Difference
					Lower	Upper
FAMILY INCOME IN CONSTANT $	21.022	469	.000	26940.207	24828.15	29052.26

 

 

Yale University. (1997). Confidence Intervals. Retrieved December 24, 2020, from http://www.stat.yale.edu/Courses/1997-98/101/confint.htm

LaTonya

The variable or population, the total set of individuals, objects, groups, or events in which the researcher is interested (Frankfort-Nachmias et. al, 2020 p.179) reviewed for the assignment is family income in constant$.  The mean age for the respondents is 48.5.  The data below is the sample size 100 with a 90% and 95% confidence interval (CI), a range of values defined by the confidence level within which the population parameter is estimated to fall (Frankfort-Nachmias et. al, 2020, p.212) is below. 

Descriptives
	Statistic
FAMILY INCOME IN CONSTANT $	Mean	27664.74
	90% Confidence Interval for Mean	Lower Bound	23037.63
		Upper Bound	32291.84

 

Descriptives
	Statistic
FAMILY INCOME IN CONSTANT $	Mean	27664.74
	95% Confidence Interval for Mean	Lower Bound	22134.17
		Upper Bound	33195.31

 

 

            The data below is the sample size of 400 and the CI of 90 % and 95%

 

Descriptives
	Statistic
FAMILY INCOME IN CONSTANT $	Mean	27568.28
	90% Confidence Interval for Mean	Lower Bound	25097.78
		Upper Bound	30038.78

 

 

Descriptives
	Statistic
FAMILY INCOME IN CONSTANT $	Mean	27568.28
	95% Confidence Interval for Mean	Lower Bound	24622.21
		Upper Bound	30514.35

 

The results of the sample of 100 with CI 90 % and 95%

 

Upper              $32,291.84                              $33,195.31

 

Lower              $23,037.63                              $22,134.17

 

Width              $9,254.21                                $11,061.14

 

 

The results of the sample of 400 with CI 90% and 95%

 

Upper              $30,038.78                              $30,514.35

 

Lower              $25,097.78                              $24,622.21

 

Width              $4,941                                     $5,892.41

 

 

            The results of data show the increase in the sample size reduces the width of the CI, which means the CI is more precise, or the reduction of our margin of error.  The population’s family income will fall between the upper and lower. 

 

 

Reference

Frankfort_Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society

                (9th ed.). Thousand Oaks, CA: Sage Publications.