# Statistics: paried observations

• k77i
In summary, 10 people were randomly selected to take a cholesterol-lowering medication and their LDL levels were measured before and after. The mean difference between before and after was -122.586 but the correct interval was (8.5,31.5).
k77i

## Homework Statement

To test the efficacy of a new cholesterol-lowering medication, 10 people are selected at random. Each has their LDL levels measured (shown below as Before), then take the medicine for 10 weeks, and then has their LDL levels measured again (After).

Before After
195 175
131 129
141 105
182 184
173 138
123 120
147 115
156 144
125 87
161 137

Give a 95.8% confidence interval for meanB - meanA , the difference between LDL levels before and after taking the medication.

## Homework Equations

d(bar) - t(alpha/2)(Sd/sqrt(n)) < meanDifference < d(bar) + t(alpha/2)(Sd/sqrt(n))

## The Attempt at a Solution

I found all the values using excel:

d(bar) = 20
t(alpha/2) = 2.368676
Sd = 190.36
n = 10 (given)

and my answer was (-122.586 < meanDifference < 162.586)

but this is incorrect

k77i said:

## Homework Statement

To test the efficacy of a new cholesterol-lowering medication, 10 people are selected at random. Each has their LDL levels measured (shown below as Before), then take the medicine for 10 weeks, and then has their LDL levels measured again (After).

Before After
195 175
131 129
141 105
182 184
173 138
123 120
147 115
156 144
125 87
161 137

Give a 95.8% confidence interval for meanB - meanA , the difference between LDL levels before and after taking the medication.

## Homework Equations

d(bar) - t(alpha/2)(Sd/sqrt(n)) < meanDifference < d(bar) + t(alpha/2)(Sd/sqrt(n))

## The Attempt at a Solution

I found all the values using excel:

d(bar) = 20
t(alpha/2) = 2.368676
Sd = 190.36
n = 10 (given)

and my answer was (-122.586 < meanDifference < 162.586)

but this is incorrect

I don't know what your Sd is, but if it is the sample standard deviation of the difference, then it is wrong. I get sample mean difference = m = 20, sample standard dev. of diff. = s = 15.3695 (your Sd?). This gives a confidence interval very different from yours.

RGV

yes it was the standard deviation of the means and I don't get why it would be wrong, I used excel to calculate it..

Anyways the correct interval was (8.5,31.5)

I first used Maple to do the calculation. Then, to see if Excel was giving you the trouble, I re-did the analysis using Excel. It agreed with the Maple calculation and disagreed with yours. I suggest you search for a typo or something similar.

## What is the definition of paired observations in statistics?

Paired observations in statistics refer to a type of data analysis where two sets of data are collected from the same subjects or units, and each data point in one set is directly related to a data point in the other set. This allows for direct comparison of the data points and can provide more accurate results.

## Why are paired observations important in statistical analysis?

Paired observations are important because they can reduce the influence of individual differences and other external factors on the data. By using paired data, researchers can control for these variables and make more accurate conclusions about the relationship between the two sets of data.

## How are paired observations analyzed in statistics?

Paired observations can be analyzed using various statistical methods such as paired t-tests, Wilcoxon signed-rank tests, and ANOVA. These tests help determine if there is a significant difference between the two sets of data and can provide insights into the relationship between the variables.

## What are some examples of paired observations in real-world applications?

Paired observations can be found in many areas of research, such as in medical studies where the same group of patients is given two different treatments and their outcomes are compared. They can also be used in marketing research, where the same group of participants is shown two different advertisements and their responses are recorded.

## What are the potential limitations of using paired observations in statistical analysis?

One limitation of paired observations is that they may not be suitable for all types of research questions. Additionally, if the pairing is not done correctly, it can lead to biased results. Paired observations also require a larger sample size compared to independent observations to achieve the same level of statistical power.

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