If n=10, ¯ x (x-bar)=48, and s=17, construct a confidence interval at a 95% confidence level. Assume the data came from a normally distributed population.

Answer 1

So, let us go over our inputs:

1. n = 10
2. sample mean = 48
3. sample s.d. = 17

Let us first find the standard error before we construct the confidence interval:

SE = sample s.d. / sqrt (n)

SE = 17 / sqrt (10)

SE = 5.37587

Now, to construct a 95% confidence interval, we know the formula is:

sample mean ± 1.96 × standard error

48 ± 1.96 × 5.37587

48 ± 10.5367052

Thus our confidence interval is (37.4633,58.5367).