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]

Would it be appropriate to use the
Student's t- distribution to construct a confidence interval for these data?

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]

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

thats right, and that's 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]

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

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.