inferential statistics is constructing a confidence interval.

The makers of a soft drink want to identify the average age of its consumers. A sample of 16 consumers is taken. The average age in the sample was 22.5 years with a standard deviation of 5 years.
1. Construct a 95% confidence level.
2. Now do the same thing with 80% confidence level.

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... α = .025
Therefore, t.025 = 2.132
Note: α = .025 (i.e., 2.5 % of one tail end of the normal distribution) because it represents either the lower or upper end of an overall 95% confidence interval.

4. Use confidence interval formula

sample mean - (t.025 )(SEM) ≤ μ ≤ sample mean + (t.025 )(SEM)

22.5 - (2.132)(1.25) ≤ μ ≤ 22.5 + (2.132)(1.25)

22.5 - ...