Tdistribution to construct a confidence interval question

In summary, a T-distribution is a probability distribution used for estimating population parameters with small sample sizes or unknown population standard deviation. It is similar to a normal distribution but has heavier tails. It is used to construct confidence intervals by providing critical values based on sample size and confidence level. As sample size increases, the T-distribution approaches a normal distribution. Higher confidence levels result in wider intervals. The T-distribution can be used for various types of data, but assumptions and conditions should be checked beforehand.
  • #1
joe98
27
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
 
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  • #2
Any thoughts guys?
 
  • #3
Any ideas guys?
 

Related to Tdistribution to construct a confidence interval question

1. What is a T-distribution?

A T-distribution, also known as a Student's t-distribution, is a probability distribution that is used to estimate population parameters when the sample size is small or when the population standard deviation is unknown. It is similar to a normal distribution, but it has heavier tails, making it more suitable for small sample sizes.

2. How is a T-distribution used to construct a confidence interval?

A T-distribution is used to construct a confidence interval by providing critical values based on the sample size and the desired confidence level. These critical values are used to calculate the upper and lower bounds of the confidence interval, which is a range of values within which the true population parameter is likely to fall.

3. What is the relationship between sample size and the T-distribution?

The T-distribution is heavily influenced by sample size. As the sample size increases, the T-distribution approaches a normal distribution. This means that for larger sample sizes, the critical values for the T-distribution will be closer to those of a normal distribution, and the confidence interval will be narrower.

4. How does the confidence level affect the T-distribution?

The confidence level reflects the probability that the true population parameter falls within the calculated confidence interval. A higher confidence level, such as 95%, means that there is a higher probability that the true population parameter is within the interval. This affects the critical values used in the T-distribution and results in a wider confidence interval.

5. Can the T-distribution be used for any type of data?

The T-distribution is most commonly used for continuous, numerical data that follows a normal distribution. However, it can also be used for non-normal data, as long as the sample size is large enough. It is important to check the assumptions and conditions before using the T-distribution to ensure accurate results.

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