Tdistribution to construct a confidence interval question

Click For Summary
SUMMARY

The discussion centers on the appropriateness of using the Student's t-distribution to construct a confidence interval for a dataset with a sample size of 10, a mean of 8.905, and a standard deviation of 9.690. It is established that the t-distribution is suitable due to the small sample size (n < 40) and the requirement for the population to be normally distributed. Participants emphasize the importance of normality in the underlying population for valid inference using the t-distribution.

PREREQUISITES
  • Understanding of Student's t-distribution
  • Knowledge of confidence intervals
  • Familiarity with sample size implications in statistics
  • Concept of normal distribution
NEXT STEPS
  • Study the properties of the Student's t-distribution
  • Learn how to calculate confidence intervals using the t-distribution
  • Explore the Central Limit Theorem and its implications for sample sizes
  • Investigate methods to assess normality in data distributions
USEFUL FOR

This discussion is beneficial for statisticians, data analysts, and students studying inferential statistics, particularly those interested in constructing confidence intervals with small sample sizes.

joe98
Messages
26
Reaction score
0
The following are summary statistics for a data set. Would it be appropriate to use the
Student's t- distribution to construct a confidence interval for these data?
Explain clearly!

Sample size = 10
Mean = 8.905
Median = 6.105
Standard deviation = 9.690
Minimum = 0.512
Maximum = 39.920
Q1 = 1.967
Q3 = 8.103

My answer would be it would be appropriate since n is less than 40(small sample size), we can use t distribution

also the population should be normally distributed

Any other explanations guys
 
Physics news on Phys.org
Any thoughts guys?
 
Any ideas guys?
 

Similar threads

Undergrad Student's t- distribution to construct a confidence interval question
  • · Replies 4 ·
Replies
4
Views
5K
Conceptual Question Dealing with Confidence Intervals
  • · Replies 3 ·
Replies
3
Views
2K
95% confidence interval on the mean
  • · Replies 3 ·
Replies
3
Views
2K
The Meaning of a 95% T Confidence Interval for the Mean
  • · Replies 4 ·
Replies
4
Views
2K
MHB Confidence interval of difference
  • · Replies 1 ·
Replies
1
Views
1K
MHB Determine the confidence interval
  • · Replies 3 ·
Replies
3
Views
1K
Confusion between z and t values
  • · Replies 5 ·
Replies
5
Views
3K
Finding a confidence interval.
  • · Replies 1 ·
Replies
1
Views
7K
Prediction interval - what did I do wrong?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Confidence interval on Standard deviation
  • · Replies 4 ·
Replies
4
Views
2K