Question

if n=28, $\bar{x}$(x - bar)=30, and s=10, construct a confidence interval at a 90% confidence level. assume the data came from a normally distributed population. give your answers to one decimal place. < $mu$ < question help: message instructor post to forum submit question

Explanation:

Step1: Determine degrees of freedom

$df=n - 1=28 - 1 = 27$

Step2: Find the t - value

For a 90% confidence level and $df = 27$, from the t - distribution table, $t_{\alpha/2}=1.703$

Step3: Calculate the margin of error

$E=t_{\alpha/2}\frac{s}{\sqrt{n}}=1.703\times\frac{10}{\sqrt{28}}\approx1.703\times\frac{10}{5.2915}\approx3.22$

Step4: Construct the confidence interval

The lower limit is $\bar{x}-E=30 - 3.22 = 26.8$
The upper limit is $\bar{x}+E=30 + 3.22 = 33.2$

Answer:

$26.8<\mu<33.2$