Question

Give a real world example of where you would have to use Student’s t because getting a large sample would be either impossible, dangerous, or very costly.

Pick a level of confidence (90% - 99.9%) for a confidence interval.

Pick a sample size (between 9 and 39)

Compare / contract the critical t-value with the critical z-value for your scenario.

Answer 1

Real world example where we would use Student's t :

Systolic blood pressure of n = 10 persons is given below:
n = Sample Size = 10

= Sample Mean = 121.2

Case 1: To calculate critical t values:

s = Sample SD = 11.1

SE = s/

= 11.1/ = 3.5101

Pick level of confidence = 95%

So,

= 0.05

ndf = 10 - 1 = 9

From Table,critical values of t = 2.2622

Case 2: To calculate critical Z values:

s = Sample SD = 11.1

SE = s/

= 11.1/ = 3.5101

Pick level of confidence = 95%

So,

= 0.05

From Table,critical values of Z = 1.96

So,

Compare/ contrast :

Critical t values: 2.2622

Critical Z values = 1.96

By comparison, we note that Critical t values are greater than Critical Z values.