Assume simple random sampling. Calculate the confidence...

Assume simple random sampling. Calculate the confidence interval for the population total for each of the following.
a. $N=1325 ; n=121 ; s=20 ; \bar{x}=182$;
$ 95\%$ confidence level
b. $N=2100 ; n=144 ; s=50 ; \bar{x}=1,325$;
$98 \%$ confidence level

Key Concepts

Confidence Interval

A confidence interval is a range of values derived from sample data that is likely to contain the true population parameter with a specified level of confidence. It quantifies the uncertainty associated with an estimate, allowing researchers to make probabilistic statements about the accuracy and precision of their findings.

Population Total Estimation

Population total estimation involves extending the sample findings to estimate the total sum of a variable for the whole population. In sampling theory, this is typically done by multiplying the sample mean by the population size, and adjustments are then made using the confidence interval to reflect sampling variability.

Simple Random Sampling

Simple random sampling is a sampling technique where every member of the population has an equal chance of being selected. This method helps to ensure the sample is representative of the population, which is a prerequisite for the validity of statistical inferences, including the calculation of confidence intervals.

Finite Population Correction

When sampling is performed without replacement from a finite population, the finite population correction (FPC) is used to adjust the standard error. This correction accounts for the reduced variability resulting from the limited size of the population, providing a more accurate confidence interval when the sample size is a significant fraction of the total population.

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