Confident Interval

Confident Interval

Since calculating a population mean is cumbersome, a sample mean is used to give an estimate of the population or true mean. Confident interval provides a range of values within which a certain parameter is likely to lie. At a 95% confidence interval, we are 95% certain that a true mean of the population is lies within a given range from the sample mean. There is only a 5% chance that a population mean is outside the given range (Thangjai, Niwitpong, & Niwitpong, 2017). However, a 99% confidence interval means that estimated value is just within a plus or minus 1% margin of error. Therefore, we are 99% certain that sample estimate is correct; hence there is a 1% chance that estimated values of the true mean are not accurate.

Regarding the heartbeat, we are 95% confidence that true male heartbeat at resting lies within plus or minus 1.42 from the sample mean (79.88±1.42).  Therefore, we are 95% certain that male heartbeat at resting lies between 81.3 and 7946 mean values. The population heartbeat mean for male after exercise must lie between 90.1±1.51. Similarly, the mean heartbeat of the female population at resting must range between a value of 1.54 from the sample mean of 80.94 (80.94±1.54) while the mean value of female heartbeat after exercise deviates from the sample mean by 2.12 (89.97±2.12). We are, therefore, 95% sure that a true female heartbeat mean after exercise lies within the given interval.

However, at a 99% confidence interval, the margin of error is reduced; hence the range and margin error are larger than 95% confidence interval (Thangjai, Niwitpong, & Niwitpong, 2017). The heartbeat for the male at resting has a higher margin of error of 1.88 compared to 1.42 for 99% and 95% respectively. Consequently, the mean heartbeat ranges between 81.77 and 77.99 at a 99% confidence interval compared to 81.3 and 78.46 for 95% confidence interval. We also notice a similar trend in other variables. For instance, Male heartbeat after exercise is higher for 99% than 95% confidence interval (1.99 compared to 1.51). The margin of error heartbeat mean for female at resting and after exercise was 2.04 and 2.81 at 99% respectively. These values are higher than 1.54 and 2.12 for female at resting and after exercise at a 95% confidence interval. Therefore, despite using the same sample mean, standard deviation, and sample size, the 99% confident interval has a higher margin of error than 95% confidence interval (Dunn et al., 2016). Therefore, a higher range of mean heartbeat values across the variables is attributed to the higher margin of error in 99% than 95% confidence intervals.

Conclusion

The confident interval is used to estimate the stability of the sample estimate. The commonly used are 95% and 99% confidence intervals. Typically, a 99% confidence interval has a higher range and margin of error than a 95% confidence interval. Ideally, as the scientific error reduces, the population mean is spread over a broader scale.

References

Dunn, P. K., Carey, M. D., Richardson, A. M., & McDonald, C. (2016). Learning the Language of Statistics: Challenges and Teaching Approaches. Statistics Education Research Journal, 15(1).

Thangjai, W., Niwitpong, S. A., & Niwitpong, S. (2017). Confidence intervals for the common mean of several normal populations. In Robustness in Econometrics (pp. 321-331). Springer, Cham.