Question

In: Statistics and Probability

In a random sample of 23 ​people, the mean commute time to work was 31.2 minutes...

In a random sample of 23 ​people, the mean commute time to work was 31.2 minutes and the standard deviation was 7.3 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 98​% confidence interval for the population mean μ. What is the margin of error of μ​? Interpret the results.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean =    = 31.2

Population standard deviation =    = 7.3

Sample size = n =23

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

Margin of error = E = Z/2    * ( /n)

= 2.326 * ( 7.3/  23 )

= 3.54
At 98% confidence interval estimate of the population mean
is,

- E < < + E

31.2 - 3.54 <   < 31.2+ 3.54

27.66 <   < 34.74

(27.66 , 34.74)


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