Question

In a random sample of 8 people, the mean commute time to work was 34.5 minutes and the standard deviation was 7.4 minutes. A 90​% confidence interval using the​ t-distribution was calculated to be left parenthesis 29.5 comma 39.5 right parenthesis(29.5,39.5). After researching commute times to​ work, it was found that the population standard deviation is 9.3minutes. Find the margin of error and construct a 90​% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.

The margin of error of mu?

Answer 1

Given information:

For 90% confidence interval, using excel function "=NORMSINV(0.95)", critical value of z is $z_{\alpha/2}=z_{c}=1.645$ . So required confidence interval is

$\bar{x}\pm z_{critical}\frac{\sigma}{\sqrt{n}}=34.5\pm 1.645\cdot \frac{9.3}{\sqrt{8}}=34.5\pm 5.4=(29.1,39.9)$

The margin of error is:

ME = 5.4

Lower limit: 29.1

Upper limit: 39.9