Question

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate:

(a) find the critical value t Subscript alpha divided by 2​, ​
(b) find the critical value z Subscript alpha divided by 2​, or​
(c) state that neither the normal distribution nor the t distribution applies.

Answer 1

Answer: Option 'a' is correct.

Explanation:

To construct a confidence interval, we have four steps to do:

1) Recognise the sample statistic by calculating the sample mean and sample variance.

2) Recognise the confidence level i.e. 90%, 95% etc.

3) Calculate the margin of error :

As we know that Margin of error = Critical value × Standard deviation

Now, critical value in case of t - test,

`t_{(\alpha)/(2),v}`

4) find the confidence interval which is given below:

Confidence interval = Margin of error + Sample statistics

So, Option 'a' is correct.