How Do I Calculate Confidence Intervals for Two Means?

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To calculate confidence intervals for two means, start by determining the means (barX1 and barX2) of your two samples. The difference in means can be modeled using the normal distribution, where the standard error is calculated as the square root of the sum of the variances divided by their respective sample sizes. Use a Z-value of ±1.96 for a 95% confidence level to establish the confidence interval. The formula for the confidence interval is (barX1 - barX2) ± Z * (sqrt(sd1^2/n1 + sd2^2/n2)). Visualizing the data with a graph can also aid in understanding the differences.
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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