A random sample of one hundred was taken, and the quantitative variable selected was “AGE OF RESPONDENT.” Upon a descriptive statistics analysis on the random sample at a 95 percent confidence interval, it was found that with a 95 percent degree of confidence, the true mean value of the age of the respondents falls between 44.62 and 51.38.

Furthermore, there is a 90 percent degree of confidence that the true mean value of the respondents’ ages falls between 45.17 and 50.83. Therefore, a reduction in the degree of confidence from 95 percent to 90 percent increased the confidence interval of the mean from 6.76 and to 11.17. The same was observed when a random sample of four hundred was taken whereby the true mean value was found to fall between 48.14 and 51.51at a 95 percent degree of confidence and 48.41 and 51.24at a 90 percent degree of certainty.

## Table 1: Descriptive Statistics SPSS Example of 100 at a 95 Percent Degree of Confidence

Descriptives | ||||
---|---|---|---|---|

Statistic | Std. Error | |||

Mean | 48.00 | 1.702 | ||

95% Confidence Interval for Mean | Lower Bound | 44.62 | ||

Upper Bound | 51.38 | |||

5% Trimmed Mean | 47.61 | |||

Median | 48.50 | |||

Variance | 289.657 | |||

AGE OF RESPONDENT | Std. Deviation | 17.019 | ||

Minimum | 19 | |||

Maximum | 87 | |||

Range | 68 | |||

Interquartile Range | 26 | |||

Skewness | .294 | .241 | ||

Kurtosis | -.560 | .478 |

## Table 2: Descriptive Statistics SPSS Example of 100 at a 90 Percent Degree of Confidence

Descriptive | ||||
---|---|---|---|---|

Statistic | Std. Error | |||

Mean | 48.00 | 1.702 | ||

90% Confidence Interval for Mean | Lower Bound | 45.17 | ||

Upper Bound | 50.83 | |||

5% Trimmed Mean | 47.61 | |||

Median | 48.50 | |||

Variance | 289.657 | |||

AGE OF RESPONDENT | Std. Deviation | 17.019 | ||

Minimum | 19 | |||

Maximum | 87 | |||

Range | 68 | |||

Interquartile Range | 26 | |||

Skewness | .294 | .241 | ||

Kurtosis | -.560 | .478 |

## Table 3: Descriptive Statistics SPSS Example of 400 at a 95 Percent Degree of Confidence

Descriptives | ||||
---|---|---|---|---|

Statistic | Std. Error | |||

Mean | 49.82 | .858 | ||

90% Confidence Interval for Mean | Lower Bound | 48.14 | ||

Upper Bound | 51.24 | |||

5% Trimmed Mean | 49.68 | |||

Median | 49.00 | |||

Variance | 293.582 | |||

AGE OF RESPONDENT | Std. Deviation | 17.134 | ||

Minimum | 18 | |||

Maximum | 89 | |||

Range | 71 | |||

Interquartile Range | 27 | |||

Skewness | .109 | .122 | ||

Kurtosis | -.885 | .244 |

## Table 4: Descriptive Statistics SPSS Example of 400 at a 90 Percent Degree of Confidence

Descriptives | ||||
---|---|---|---|---|

Statistic | Std. Error | |||

Mean | 49.82 | .858 | ||

90% Confidence Interval for Mean | Lower Bound | 48.41 | ||

Upper Bound | 51.51 | |||

5% Trimmed Mean | 49.68 | |||

Median | 49.00 | |||

Variance | 293.582 | |||

AGE OF RESPONDENT | Std. Deviation | 17.134 | ||

Minimum | 18 | |||

Maximum | 89 | |||

Range | 71 | |||

Interquartile Range | 27 | |||

Skewness | .109 | .122 | ||

Kurtosis | -.885 | .244 |

Confidence interval is the range of values that a true parameter lies at a given degree of confidence. Furthermore, the confidence interval’s width reduces with the increase in sample size as larger samples tend to be more reliable than smaller samples; therefore, the uncertainty of the true value of the mean reduces. This indicates that researchers are underutilized in confidence intervals while attempting to generalize the characteristics of a given sample to the rest of the population.

The selected degree of confidence determines how much standard error they are willing to accept depending on the use of the study and the precision required. Therefore, variability, confidence level, and sample size significantly impact the width of the interval, which indicates the uncertainty that a researcher is willing to accommodate in generalizing the characteristics of a sample to the rest of the population.

**References**

Fox, J. (1991). Discrete data. In Regression diagnostics (pp. 62-66). SAGE Publications, Inc.

**Appendices**

[RandomSampleOf100]

**Case Processing Summary**

Case Processing Summary | ||||||
---|---|---|---|---|---|---|

Cases | Valid | Missing | ||||

N | Percent | N | Percent | N | Percent | |

AGE OF RESPONDENT | 399 | 99.8% | 1 | 0.3% | 400 | 100.0% |