1) 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.
Indicate whether or not it is appropriate to use the t-distribution.
Yes / No
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 =
2) Is a t-Distribution Appropriate?
A sample with size n=10 has x¯=508.5, and s=21.5. The dotplot for this sample is given below.
Indicate whether or not it is appropriate to use the t-distribution.
Yes / No

In the first test t distribution is appropriate to use because in the dot plot the 16 data points can be seen other the the data points clustered round the mean.

Here degrees of freedom = n-1= 74

S. E= s/√n

S.E= 10.1/ √74= 1.17

For t - distribution it is assumed that the sample is approximately normal which is visible in the dot plot in the first test.

In the second case z test should be applied.

Z test is used when the population standard deviation is not known .

In the second test t distribution is not appropriate to use because in the dot plot only 2 data points can be seen other the the data points clustered round the mean.

For t - distribution it is assumed that the sample is approximately normal which is not visible in the dot plot.