Answered: In a random sample of 8 people, the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 90% confidence interval using the t-distribution was calculated to be (29.6,39.4). After researching commute times to work, it was found that the population standard deviation is 9.7 minutes. 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 μ is ___

A 90% confidence interval using the standard normal distribution is ( __ , __ )

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

$Given sample size (n) = 8 Mean (x) = 34.5 standard deviation (s) = 7.3 confidence level = 90 % 90 % confidence interval using the t - distribution was calculated to be (29.6, 39.4) After researching commute times to work population standard deviation (σ) = 9.7$