Respond to one of your colleagues posts and explain how you might see the implications differently.
Random sample of 100:
Statistics
AGE OF RESPONDENT
N
Valid
88
Missing
0
Mean
47.56
Std. Deviation
17.312
Range
68
Minimum
21
Maximum
89
Descriptive
Statistic
Std. Error
FAMILY INCOME IN CONSTANT DOLLARS
Mean
41925.36
3872.849
95% Confidence Interval for Mean
Lower Bound
34221.03
Upper Bound
49629.69
5% Trimmed Mean
37636.81
Median
33255.00
Variance
1244913697.655
Std. Deviation
35283.335
Minimum
1478
Maximum
160742
Range
159264
Interquartile Range
40645
Skewness
1.846
.264
Kurtosis
4.201
.523
Descriptive
Statistic
Std. Error
FAMILY INCOME IN CONSTANT DOLLARS
Mean
41925.36
3872.849
90% Confidence Interval for Mean
Lower Bound
35482.30
Upper Bound
48368.43
5% Trimmed Mean
37636.81
Median
33255.00
Variance
1244913697.655
Std. Deviation
35283.335
Minimum
1478
Maximum
160742
Range
159264
Interquartile Range
40645
Skewness
1.846
.264
Kurtosis
4.201
.523
Random Sample of 400:
Statistics
AGE OF RESPONDENT
N
Valid
340
Missing
2
Mean
48.17
Std. Deviation
17.304
Range
70
Minimum
19
Maximum
89
Descriptive
Statistic
Std. Error
FAMILY INCOME IN CONSTANT DOLLARS
Mean
40806.53
2052.001
95% Confidence Interval for Mean
Lower Bound
36768.97
Upper Bound
44844.09
5% Trimmed Mean
36426.80
Median
33255.00
Variance
1313741394.041
Std. Deviation
36245.571
Minimum
370
Maximum
160742
Range
160373
Interquartile Range
34179
Skewness
1.760
.138
Kurtosis
3.391
.275
Descriptive
Statistic
Std. Error
FAMILY INCOME IN CONSTANT DOLLARS
Mean
40806.53
2052.001
90% Confidence Interval for Mean
Lower Bound
36774.09
Upper Bound
43180.50
5% Trimmed Mean
36426.80
Median
33255.00
Variance
1313741394.041
Std. Deviation
36245.571
Minimum
370
Maximum
160742
Range
160373
Interquartile Range
34179
Skewness
1.760
.138
Kurtosis
3.391
.275
The variable selected for this discussion was family income in constant dollars. For the sample of 100, at a 95% confidence interval, the lower bound is calculated as $34,221.03 and the upper bound is $49,629.69. At a 90% confidence interval, the lower bound is calculated as $35,482.30 while, the upper bound is $48,368.43.
The differences in the upper bound and lower bound amounts is the results of the change in the range of values determined to capture the true parameter for which the population is found. According to Frankfort-Nachmais (2020), when estimating values of a sample statistic, utilizing confidence intervals increases the accuracy of the population parameter therefore, we can accurately estimate the population parameter is found within the confidence intervals for this variable.
When we compare the change in the sample size, we can also see the differences in the values found. For the sample of 400, at a 95% confidence, the lower bound is calculated at $36,768.97 and the upper bound at $44,844.09. At a 90% confidence interval, the lower bound is $36,774.09 while, the upper bound is $43,180.50. Much like the sample of a 100, the lower and upper bounds are different due to the change in the range.
However, the large sample size improves the accuracy of the confidence interval. According to du Prel et al (2009), the values within the upper and lower bound are representative of the value of the population parameter while those outside the interval are not excluded however, considered improbable. The larger the sample size therefore, the increased likelihood the values within the interval are more accurate in representing the population. In research, it can be suggested that confidence intervals are underutilized. When considering the information above regarding the sample size and the purpose of confidence intervals, implications for underutilizing confidence intervals become apparent. The purpose of using a confidence interval is that it assists with making a statement about a population since the information is supported by the mean, size, and standard deviation of the sample from the population. Therefore, if we were to studying poverty levels and the percentage of society which are affected by poverty, the use of confidence intervals could be used to explain the interval of family income which applies to those impacted by poverty.
