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# A common problem in inferential statistics is constructing a confidence interval.

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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.

https://brainmass.com/statistics/confidence-interval/inferential-statistics-constructing-confidence-interval-3246

#### Solution Preview

Part One (for 95% confidence interval):

1. Calculate the estimated standard error of the mean ('SEM'):

SEM = standard deviation / square root ('SQRT') of sample size = 5 / SQRT(16) = 1.25

2. Calculate df:

df = n-1 = 16-1 = 15

3. Determine t value for 95% confidence:

Use Student's t distribution table to determine t, using df =15 ...

#### Solution Summary

The solution addresses 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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