Question

Is a t-Distribution Appropriate?

A sample with size n=75 has x¯=18.92, and s=10.1. The dotplot for this sample is given below.

If it is appropriate, give the degrees of freedom for the t-distribution and give the estimated standard error. If it is not appropriate, enter -1 in both of the answer fields below.

Enter the exact answer for the degrees of freedom and round your answer for the standard error to two decimal places.
DF=

Standard Error=

Answer 1

A sample with size n=75 has x¯=18.92, and s=10.1.

Since we have sufficient large sample size n = 75 ( n>30 ) , bu we are given sample standard deviation , population standard deviation is not known , so we use t-distribution here .

Yes , t-Distribution Appropriate .

Degrees of freedom for the t-distribution are given by n-1 ,

So DF = n-1 = 75-1 = 74

Estimated standard error (SE) is given by SE =

SE = = = 1.166248

Hence

DF = 74

Standard Error = 1.17                    [ rounding to two deciamals ]