# Student's t- distribution to construct a confidence interval question

1. Mar 9, 2012

### joe98

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.

Any other explanations guys

2. Mar 9, 2012

### Stephen Tashi

A confidence interval for what? The mean of the population they were sampled from?

This is a homework type problem, right? We begin to see why homework section wants such problems posed in a orderly format that includes a complete statement of the problem.

I suppose the issue here might be how much your numerical tables for the t-statistic depend on the population being normally distributed and whether you think your sample is.from a normally distributed population.

3. Mar 9, 2012

### joe98

thats right, and thats the data given in the question,

the question says if it is suitable to use t distribution to construct a confidence interval using the given data.

Somehow i have to explain how its possible?

Any ideas?

4. Mar 9, 2012

### joe98

so Stephen, your suggesting its not suitable to use tdistribution because its not normally disstributed but could there be any other reasons?

5. Mar 12, 2012

### camillio

Joe, just simply look how t distribution looks. Is it symmetric? What about other properties? Do your data look like samples from this distribution? Etc.