Question

The following summary statistics were calculated for a continuous variable in a particular data set; n=10, mean=8.90, sd=9.69, median=6.105, min=0.512, max=39.92, Q1=1.967, Q3=8.103. Would it be appropriate to use the Student’s t distribution to construct a confidence interval for the population mean from these data?

i) yes;

or ii) no;

or iii) possibly, following a suitable transformation?

Answer 1

Since we know that, Student's t-distribution is a probability distribution that is used to estimate population parameters when the sample size is small and when the population variance is unknown.

In this case we see that our sample size n=10 (< 30) is small and population standard deviation is unknown and sample standard deviation is known which is 9.69.

Thus we can conclude that, Students t distribution is appropriate  to construct a confidence interval for the population mean from these given data.

Hence option (1) is correct answer.