Question

In a random sample of 20 ​people, the mean commute time to work was 31.7 minutes and the standard deviation was 7.3 minutes. assume the population is normally distributed and use a​ t-distribution to construct a 95​% confidence interval for the population mean mu. what is the margin of error of mu​? interpret the results.

Answer 1

Solution: We are given:

x bar=31.7

s = 7.3

n=20

The 95% confidence interval for the population mean is given below:

xbar +- $t_{\frac{0.05}{2}}$ $\frac{s}{\sqrt{n}}$

31.7 +- (2.093 x $\frac{7.3}{\sqrt{20}}$)

31.7 +- 3.42

[31.7-3.42,31.7+3.42]

[28.28 ,35.12 ]

Therefore the 95% confidence interval for the population mean is:

28.28≤μ≤35.12

The margin of error is 3.42

There is 95% chance that the confidence interval 28.28≤μ≤35.12 contains the true population mean.