Given:
sample size - 26
sample mean - $154
population standard deviation - $17
Find: 95% confidence interval
Solution:
To determine the confidence interval, we use the formula below.
[tex]CI=\bar{x}\pm t(\frac{\sigma}{\sqrt{n}})[/tex]where:
bar x = sample mean
t = critical value at a given percentage
σ = population standard deviation
n = sample size
Let's now solve for the confidence interval. Recall that at a 95% confidence interval, the t-value is 2.06. We are using the t-value since the sample size is less than 30.
1. Divide the population standard deviation by the square root of the sample size.
[tex]17\div\sqrt{26}\Rightarrow17\div5.099019=3.33397[/tex]2. Multiply the quotient by the t-value.
[tex]3.33397\times2.06\approx6.87[/tex]3. Add and subtract the product from the sample mean.
[tex]154-6.87=147.13[/tex][tex]154+6.87=160.87[/tex]Therefore, the 95% confidence interval to estimate the population mean is between $147.13 to $160.87
