How Do I Calculate Confidence Intervals for Two Means?

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SUMMARY

This discussion focuses on calculating confidence intervals for the difference between two means, specifically using the formula for the normal distribution. The key components include the means (barX1 and barX2), standard deviations (sd1 and sd2), and sample sizes (n1 and n2). The Z value for a 95% confidence level is established as ±1.96. The formula provided is (barX1 - barX2) ± z * sqrt(sd1²/n1 + sd2²/n2), which defines the confidence interval for the difference between the two means.

PREREQUISITES
  • Understanding of basic statistics, including means and standard deviations.
  • Familiarity with the normal distribution and Z-scores.
  • Knowledge of confidence intervals and their significance in hypothesis testing.
  • Ability to perform calculations involving sample sizes and variances.
NEXT STEPS
  • Study the derivation and application of the confidence interval formula for two means.
  • Learn about hypothesis testing and its relationship with confidence intervals.
  • Explore the use of statistical software like R or Python for calculating confidence intervals.
  • Investigate graphical representations of confidence intervals to enhance understanding.
USEFUL FOR

Statisticians, data analysts, researchers, and students who need to calculate and interpret confidence intervals for comparing two means.

girlwhoneedsmathhelp
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Here is the question I'm struggling with (Q1) :
image_123927839.JPG

I just... I just don't understand what my first step is.
Whats my barx1 and barx2? (bar x = mean, x1 = subscript 1)

My thoughts on approaching this question :
barX1 - barX2 `~ N(u1-u2, sd1^2/n1 + sd2^2/n2)
Find Z value when p = 0.975, z = + or - 1.96
Formula : (barx1-barx2)-z(root (sd1^2/n1 + sd2^2/n2) < (u1-u2) < (barx1-barx2)-z(root (sd1^2/n1 + sd2^2/n2)

Please help me! Thank you :)
 
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In this case I believe the author wants you to look at the differences directly...the random variable is ##(x_2-x_1)## and the table provides the data. Maybe draw a graph.
 

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