Question

In a random sample of 22 people, the mean commute time to work was 32.1 minutes and the standard deviation was 7.3 minutes. Assume the population is normally distributed and use a t-distribution to construct a 99% confidence interval for the population mean μ. What is the margin of error of μ? Interpret the results.

Answer #1

Solution :

Given that,

= 32.1

s = 7.3

n = 22

Degrees of freedom = df = n - 1 = 2 - 1 = 21

At1 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

_{t
/2 df} = t_{0.005,21} = 2.831

Margin of error = E = t_{/2,df}
* (s /n)

= 2.831 * (7.3/ 22) = 4.4060669

E=4.41 (rounded)

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