In a random sample of 8 people, the mean commute time to work was 35.5 minutes and the standard deviation was 7.2 minutes. A 90% confidence interval using the t-distribution was calculated to be (30.7,40.3). 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. Question content area bottom Part 1 The margin of error of μ is enter your response here. (Round to two decimal places as needed.) Part 2 A 90% confidence interval using the standard normal distribution is (enter your response here,enter your response here). (Round to one decimal place as needed.) Part 3 Compare the results. Choose the correct answer below. A. The confidence interval found using the standard normal distribution is the same as the confidence interval found using the student's t-distribution. B. The confidence interval found using the standard normal distribution is wider than the confidence interval found using the student's t-distribution. C. The confidence interval found using the standard normal distribution has smaller lower and upper confidence interval limits. D. The confidence interval found using the standard normal distribution is narrower than the confidence interval found using the student's t-distribution

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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Question content area bottom

Part 1

The margin of error of

enter your response here.

(Round to two decimal places as needed.)

Part 2

90%

confidence interval using the standard normal distribution is (enter your response here,enter your response here).

(Round to one decimal place as needed.)

Part 3

Compare the results. Choose the correct answer below.

The confidence interval found using the standard normal distribution is

the same as

the confidence interval found using the student's t-distribution.

The confidence interval found using the standard normal distribution is

wider than

the confidence interval found using the student's t-distribution.

The confidence interval found using the standard normal distribution has smaller lower and upper confidence interval limits.

The confidence interval found using the standard normal distribution is

narrower than

the confidence interval found using the student's t-distribution.

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.

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