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

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

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.

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?

joe98

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

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.