Response from week 5 classmate | RSCH 8210 – Quantitative Reasoning and Analysis | Walden University

  Respond to one of your colleague’s 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.