Question

a sample size of n=12 does not have a known population standard deviation. the population appears to be normally distributed. determine whether a margin of error should be calculated using a critical value of z a/2, a critical value of 1 a/2, or neither

Answer 1

A critical Value of ta/2

Answer 2

a critical value of z a/2

Explanation:

Given that the population appears to be normally distributed

Sample size of 12 is taken.

FOr hypothesis testing we have to calculate margin of error. Depending on the confidence level we select critical values and multiply by std error

Here though population appears to be normally distributed, we cannot take z critical value for alpha/2 since

i) sample size is very small <30

ii) Population std deviation is not known

Whenever population std deviation is not known we prefer to use t critical value instead of Z critical value.

So answer is

a critical value of z a/2