We appreciate your visit to The mean of the differences is 193 points and the standard deviation of the differences is 62 73 points The conditions for inference are met. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the correct 98% confidence interval for the mean difference in scores (after - before), follow these steps:
1. Identify the Mean and Standard Deviation:
- The mean of the differences is 193 points.
- The standard deviation of the differences is 62.73 points.
2. Determine the Sample Size:
- There are 8 students, so the sample size is 8.
3. Calculate the Standard Error:
- The standard error is calculated by dividing the standard deviation by the square root of the sample size.
- Standard Error = [tex]\( \frac{62.73}{\sqrt{8}} \)[/tex].
4. Find the t-value:
- For a 98% confidence level and degrees of freedom (df) equal to the sample size minus one (8 - 1 = 7), the t-value is 2.821. This is found using a t-table.
5. Calculate the Margin of Error:
- The margin of error is found by multiplying the t-value by the standard error.
- Margin of Error = [tex]\( 2.821 \times \text{Standard Error} \)[/tex].
6. Determine the Confidence Interval:
- Subtract the margin of error from the mean difference to find the lower limit of the confidence interval.
- Add the margin of error to the mean difference to find the upper limit of the confidence interval.
- So, the confidence interval is given by:
- Lower Limit = 193 - Margin of Error
- Upper Limit = 193 + Margin of Error
Following these steps, the 98% confidence interval for the mean difference in scores is approximately (130.43, 255.57) points.
1. Identify the Mean and Standard Deviation:
- The mean of the differences is 193 points.
- The standard deviation of the differences is 62.73 points.
2. Determine the Sample Size:
- There are 8 students, so the sample size is 8.
3. Calculate the Standard Error:
- The standard error is calculated by dividing the standard deviation by the square root of the sample size.
- Standard Error = [tex]\( \frac{62.73}{\sqrt{8}} \)[/tex].
4. Find the t-value:
- For a 98% confidence level and degrees of freedom (df) equal to the sample size minus one (8 - 1 = 7), the t-value is 2.821. This is found using a t-table.
5. Calculate the Margin of Error:
- The margin of error is found by multiplying the t-value by the standard error.
- Margin of Error = [tex]\( 2.821 \times \text{Standard Error} \)[/tex].
6. Determine the Confidence Interval:
- Subtract the margin of error from the mean difference to find the lower limit of the confidence interval.
- Add the margin of error to the mean difference to find the upper limit of the confidence interval.
- So, the confidence interval is given by:
- Lower Limit = 193 - Margin of Error
- Upper Limit = 193 + Margin of Error
Following these steps, the 98% confidence interval for the mean difference in scores is approximately (130.43, 255.57) points.
Thanks for taking the time to read The mean of the differences is 193 points and the standard deviation of the differences is 62 73 points The conditions for inference are met. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
