A question on the General Social Survey was this: "About how...

A question on the General Social Survey was this: "About how many times did you engage in intercourse during the month?" The question was only asked of participants who had previously indicated that they had engaged in sexual intercourse during the past month. The results are summarized in the Minitab output that follows: (a) Use the summary to determine the point estimate of the population mean and margin of error for the confidence interval (b) Interpret the confidence interval. (c) Verify the results by computing a $95 \%$ confidence interval with the information provided.

A question on the General Social Survey was this: "About how many times did you engage in intercourse during the month?" The question was only asked of participants who had previously indicated that they had engaged in sexual intercourse during the past month. The results are summarized in the Minitab output that follows:
(a) Use the summary to determine the point estimate of the population mean and margin of error for the confidence interval
(b) Interpret the confidence interval.
(c) Verify the results by computing a $95 \%$ confidence interval with the information provided.

Key Concepts

Confidence Interval

A confidence interval is a range of values, derived from the sample data, that is likely to contain the true population parameter. It is constructed using the point estimate and the margin of error, and it reflects the degree of uncertainty associated with the estimate.

Interpretation of a Confidence Interval

Interpreting a confidence interval involves understanding that, if the sampling process were repeated many times, a specified percentage of the calculated intervals (e.g., 95%) would contain the true population mean. This interpretation emphasizes the long-run reliability of the interval as an estimator for the population parameter.

Verification of Results through Calculation

Verification of statistical results involves recomputing the confidence interval using the provided summary statistics and the appropriate formula. This step confirms that the reported interval is accurate and aligns with the theoretical basis for constructing confidence intervals in inferential statistics.

Margin of Error

The margin of error quantifies the uncertainty associated with a point estimate. It defines the maximum expected difference between the point estimate and the true population parameter at a specified level of confidence, incorporating variability and sample size into account.

Population Mean

In statistical inference, the population mean represents the average value of a variable for the entire population. It is the parameter that researchers aim to estimate when making inferences from sample data.

Point Estimate

A point estimate is a single value that is used as an approximation of a population parameter. In the context of a confidence interval for the population mean, the sample mean is used as the point estimate because it provides the best single estimate of the true mean.

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