Question

If n=13, ¯xx¯(x-bar)=47, and s=11, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place

Answer 1

Answer

sample size n = 13

sample mean = 47

sample standard deviation = 11

confidence interval is 80%

since the population standard deviation is unknown, so we have to use t distribution instead of z distribution.

degree of freedom = n- 1= 13-1 = 12

Now, using the degree of freedom 12 and alpha level = 1 - 0.80 = 0.20 in the t distribution table, we get the following value

t critical = 1.356

Using the confidence interval formula, we can write

So, the required confidence interval for 80% confidence is (42.9, 51.1)