STA2023 Review
Confidence Intervals
Hypothesis Testing

Tuesday, June 24, 2025

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One-Sample Mean

  1. Let’s find a 95% confidence interval for wing-flap rates.
  • The 95% CI for \mu is (lower_bound, upper_bound).
  1. Perform the appropriate hypothesis test to determine if the wing-flap rate has changed. Test at the \alpha=0.10 level.
  • Hypotheses:
    • H_0: \
    • H_1: \
  • Test Statistic and p-Value
    • $t_0 = $, $p = $
  • Rejection Region
    • Reject H_0 if p < \alpha; $= $
  • Conclusion and interpretation
    • Reject or Fail to reject H_0 ($p $). There is or is not sufficient evidence to suggest the alternative hypothesis in words (not math).

Two Independent Means

  1. Use the wing-flap data to estimate the difference in apple consumption (apples) betwen those that are above or below the target rate (target). Estimate using a 95% confidence interval.
  • Thus, the 95% CI for \mu_{\text{above}} - \mu_{\text{below}} is (lower_bound, upper_bound).
  1. Perform the appropriate hypothesis test to determine if the above target pegasi are eating 5 or more apples than the below target pegasi. Test at the \alpha=0.05 level.
  • Hypotheses:
    • H_0: \
    • H_1: \
  • Test Statistic and p-Value
    • $t_0 = $, $p = $
  • Rejection Region
    • Reject H_0 if p < \alpha; $= $
  • Conclusion and interpretation
    • Reject or Fail to reject H_0 ($p $). There is or is not sufficient evidence to suggest the alternative hypothesis in words (not math).

Two Dependent Means

  1. We now want to find the 99% CI for the average improvement in wing-flap rate.
    • Hint: improvement can be measured with post - pre.
    • Hint 2: post measurement: post_training_wfr, pre measurement: pre_training_wfr.
  • The 99% confidence interval for \mu_d is (lower_bound, upper_bound).
  1. What happens if we flip the order of col1 and col2?
  • The 99% confidence interval for \mu_d is (lower_bound, upper_bound).
  1. Perform the appropriate hypothesis test to determine if there is a difference in wing-flap rate pre- and post-training. Test at the \alpha=0.01 level.
  • Hypotheses:
    • H_0: \
    • H_1: \
  • Test Statistic and p-Value
    • $t_0 = $, $p = $
  • Rejection Region
    • Reject H_0 if p < \alpha; $= $
  • Conclusion and interpretation
    • Reject or Fail to reject H_0 ($p $). There is or is not sufficient evidence to suggest the alternative hypothesis in words (not math).