Answer:
a)
[tex]z_{critical} \text{ at 0.05 level of significance } = \pm 1.96[/tex]
b)
[tex]t_{critical} \text{ at 0.05 level of significance, 14 degree of freedom } = \pm 2.144[/tex]
Step-by-step explanation:
We are given the following information in the question:
Sample size = 15
The population is normally distributed and the mean height of the population is going to be estimated with 95% confidence.
We have to find the appropriate critical value that should be used to build the 95 confidence level.
Confidence interval:
[tex]\mu \pm \text{ critical value }\frac{\sigma}{\sqrt{n}}[/tex]
If the population standard deviation is given, we use the z-critical value.
[tex]z_{critical} \text{ at 0.05 level of significance } = \pm 1.96[/tex]
If the population standard deviation is not given, we use the t-critical value.
[tex]t_{critical} \text{ at 0.05 level of significance, 14 degree of freedom } = \pm 2.144[/tex]
