Constructing a Confidence Interval for a Population Mean You intend to estimate a population mean $μ$ with the following sample.
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You believe the population is normally distributed. Find the $90 %$ confidence interval for the population mean. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places.
$90 % C.I. =$
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5. Confidence Interval: $\bar{x} \pm M E$

Steps

Step 1 ：1. Calculate sample mean $\bar{x}$ : $\frac{14 + 12 + 18 + 14 + 14 + 16 + 17 + 11 + 12 + 15 + 12 + 12}{12}$

Step 2 ：2. Calculate sample standard deviation (s): $\sqrt{\frac{Σ (x_{i} - \bar{x})^{2}}{n - 1}}$

Step 3 ：3. Find the critical t-value (t*) for a 90% confidence interval from a t-table with df = n-1 = 11

Step 4 ：4. Calculate margin of error (ME): $t * \cdot \frac{s}{\sqrt{n}}$

Step 5 ：5. Confidence Interval: $\bar{x} \pm M E$