Lecture Notes: Confidence Interval and Point Estimate for Baby Crawling Age

Overview

• Objective: Analyze data on the age (in weeks) when babies first crawl based on a survey of 12 mothers.
• Assumption: The data follows a normal distribution, allowing the calculation of confidence intervals.

Key Concepts

Point Estimate

• Task: Determine the point estimate for the mean age at which babies first crawl.
• Method: Calculate the sample mean ((\bar{x})).
  • Process:
    • Use a calculator: Enter data into a statistics calculator, utilize the one bar stat function.
    • Results:
      • Sample mean ((\bar{x})) = 38.25 weeks
      • Sample standard deviation (s) = 10.001 weeks
      • Number of data points (n) = 12

Margin of Error

• Task: Find the margin of error for a 90% confidence interval.
• Definitions:
  • Confidence Level: 90%
  • Tail Probability: 0.05 (each tail)
  • Degrees of Freedom (df): n-1 = 11
• Critical Value:
  • From statistical tables, critical value = 1.796
• Margin of Error Calculation:
  • Formula: (\text{Margin of Error} = \text{Critical Value} \times \frac{s}{\sqrt{n}})
  • Calculation yields approximately 5.18 weeks

Confidence Interval

• Task: Construct and interpret a 90% confidence interval for the true mean age.
• Confidence Interval Calculation:
  • Lower Bound = (\bar{x} - \text{Margin of Error} = 38.25 - 5.18 = 33.065) weeks
  • Upper Bound = (\bar{x} + \text{Margin of Error} = 38.25 + 5.18 = 43.435) weeks
• Interpretation:
  • We are 90% confident that the true mean age at which babies first crawl is between 33.065 weeks and 43.435 weeks.
• Units: All measurements are in weeks.