SOLUTION: In a random sample of 25 people, the mean commute time to work was 33.8 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a

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Question 1123006: In a random sample of 25 people, the mean commute time to work was 33.8 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a t-distribution to construct a 95% confidence interval for the population mean. What is the margin or error?
Answer by jim_thompson5910(35256) (Show Source):
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Use a T-table such as this one to look up the critical T value that corresponds to a 95% confidence interval.
Since n = 25 is the sample size, this means the degrees of freedom (df) is
df = n-1
df = 25-1
df = 24
Use a highlighter to mark the entire row that has df = 24.
Mark the column that is over top the 95% confidence interval.
At the intersection of this row and column is the value 2.064
This value is approximate. To get more accuracy, you'll need to use the Tinv function on your calculator.

Margin of Error = (critical T value)*(standard deviation)/sqrt(sample size)
Margin of Error = (2.064)*(7.2)/sqrt(25)
Margin of Error = (2.064)*(7.2)/5
Margin of Error = 14.8608/5
Margin of Error = 2.97216 (which is approximate)

Side Note: the mean is not used at all to compute the margin of error.