Question

In a random sample of 8 people, the mean commute time to work was 34.5 minutes and the standard deviation was 7.3 minutes. A 95% confidence interval using the t-distribution was calculated to be (28.4.40.6). After researching commute times to work, it was found that the population standard deviation is 9.4 minutes. Find the margin of error and construct a 95% 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 his (Round to two decimal places as needed.)

Answer 1

Given data: Random sample (n) = 8 Mean (x^) =34.5 Standard deviation (s)=7.3 Population Standard deviation (o)=9.4

Solution: Confidence interval (c)=95%=0.95 Significance level (a) =1-c=1-0.95=0.05 Critical value of z=2a/2=1.96(using z-value table) Margin of error (e) =z* vn = 5.06

Therefore, margin of error of u is 5.06 Z-interval of 95% confidence interval = (x^-e, x^+e) = = (34.5-5.06,34.5+5.06) = (34.5-5.06,34.5+5.06) = = (29.44, 39.56)