Confidence Interval for Mean Examples

Statistics · Axiom Academy

EXAMPLE Confidence Interval for Mean Examples Walk through constructing confidence intervals for population mean using both z-intervals and t-intervals Problem: Z-Interval (Known Population Standard Deviation) A researcher measures the IQ scores of 64 randomly selected college students and finds a sample mean of 112. The population standard deviation is known to be . Construct a 95% confidence interval for the true mean IQ. Excellent work! You've completed both confidence interval examples. Here's what we learned: Z-interval vs T-interval: Use z-interval when the population standard deviation is known; use t-interval when only the sample standard deviation is known. Critical Values: For 95% confidence, for z-intervals, but the t-critical value depends on degrees of freedom for t-intervals. Standard Error: Measures the variability of the sample mean: for z-intervals, for t-intervals. Margin of Error: The margin of error (E) determines the width of the confidence interval: wider intervals mean more uncertainty, narrower intervals mean more precision. Interpretation: We are 95% confident that the true population mean falls within the calculated interval. This does NOT mean there's a 95% probability the mean is in this specific interval! Sample Size Impact: Larger sample sizes lead to smaller standard errors and narrower confidence intervals, giving more precise estimates.

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