Confidence Interval Question help please

In summary, the question asks for the first step in finding the Z value when p = 0.975, using the formula (barx1-barx2)-z(root (sd1^2/n1 + sd2^2/n2) < (u1-u2) < (barx1-barx2)-z(root (sd1^2/n1 + sd2^2/n2). The author suggests looking at the differences directly and possibly drawing a graph.
  • #1
girlwhoneedsmathhelp
7
3
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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  • #2
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.
 

1. What is a confidence interval?

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain level of confidence. It is calculated from a sample of data and is used to estimate the true value of a population parameter.

2. How is a confidence interval calculated?

A confidence interval is calculated using the sample mean, sample standard deviation, and the desired level of confidence. The formula for calculating a confidence interval is: sample mean ± (critical value)(standard deviation/√n), where n is the sample size and the critical value is determined by the desired level of confidence and the distribution of the data.

3. What is the significance of the confidence level in a confidence interval?

The confidence level in a confidence interval represents the probability that the true population parameter falls within the calculated interval. For example, a confidence level of 95% means that if we were to repeat the sampling process multiple times, 95% of the time the true population parameter would fall within the calculated interval.

4. How does sample size affect the width of a confidence interval?

The larger the sample size, the narrower the confidence interval will be. This is because a larger sample size provides more precise estimates of the population parameter, resulting in a smaller margin of error. As the sample size increases, the margin of error decreases, making the confidence interval narrower.

5. How can confidence intervals be used in statistical inference?

Confidence intervals are used in statistical inference to make statements about the true value of a population parameter based on a sample of data. They allow us to estimate the range of values that the population parameter may fall within and make conclusions about the population based on the sample data.

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