Question 45

There is a 95% likelihood that the true population mean will fall within the confidence interval.

A confidence level of 95% indicates that there is a 95% chance the true population mean lies within the calculated confidence interval from the survey results. This reflects the reliability and precision of the data collected.

A) The results of the survey are 95% likely to accurately represent the greater population

This option is misleading as it suggests that the survey results themselves are 95% accurate in representing the population, rather than focusing on the probability that the true population mean is within the confidence interval. The confidence level pertains to the interval estimate, not the accuracy of the results themselves.

B) The results of the survey analysis will fall between 95% of the standard deviation of the mean

This statement incorrectly interprets the meaning of the confidence level. The confidence interval does not relate to the standard deviation in this way; rather, it is a range derived from the sample data that estimates where the true population parameter lies, not a measure of deviation.

C) 95% of the results of the survey would fall within the desired range of values

This option misrepresents the concept of confidence intervals. The 95% confidence level does not imply that 95% of the survey results fall within a specific range; instead, it indicates that if the same survey were repeated multiple times, 95% of the calculated intervals would contain the true population mean.

D) There is a 95% likelihood that the true population mean will fall within the confidence interval

This option accurately describes the meaning of a 95% confidence level. It conveys that there is a high probability that the interval calculated from the survey data contains the true population mean, which is the essential concept of confidence intervals in statistical analysis.

Conclusion

Option D correctly explains the meaning of a 95% confidence level, emphasizing the likelihood of the true population mean residing within the confidence interval derived from survey data. The other options misunderstand or misrepresent this statistical concept, as they focus on accuracy of results or standard deviation rather than the probability related to the population mean. Thus, D is the definitive correct choice in this context.