Question

In a random sample of 25 ?people, the mean commute time to work was 30.4 minutes and the standard deviation was 7.1 minutes. assume the population is normally distributed and use a? t-distribution to construct a 90?% confidence interval for the population mean ?. what is the margin of error of ??

Answer 1

In this problem, the given values are:

x = average = 30.4

s = standard deviation = 7.1

n = number of samples = 25

Degrees of freedom = n -1 =24

Using the t-distribution table for a normal curve at 90% CI, we get t-crit:

t-crit = 1.711

Now the Margin of Error (E) is calculated as:

E = t-crit*(s/ $\sqrt{n}$)

By substituting the known values into the equation:

E = 1.711 * (7.1/ $\sqrt{8}$)

E = +- 4.30

Therefore, the margin of error is 4.36. Hence, the commute time is between 26.1 minutes and 34.7 minutes.