Consider a random sample of size n = 31, with sample mean x = 45.5 and sample standard deviation s = 5.8.(a) Compute 90%, 95%, and 99% confidence intervals for ? using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90%95%99%lower limit upper limit (b) Compute 90%, 95%, and 99% confidence intervals for ? using Method 2 with the standard normal distribution. Use s as an estimate for ?. Round endpoints to two digits after the decimal. 90%95%99%lower limit upper limit (c) Now consider a sample size of 81. Compute 90%, 95%, and 99% confidence intervals for ? using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal. 90%95%99%lower limit upper limit Compute 90%, 95%, and 99% confidence intervals for ? using Method 2 with the standard normal distribution. Use s as an estimate for ?. Round endpoints to two digits after the decimal. 90%95%99%lower limit upper limit

The confidence interval at 90%,95% and 99% using method 1 i.e. t-distribution and method 2 i.e. th…

Answered: Consider a random sample of size n =…

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

Consider a random sample of size n = 31, with sample mean x = 45.5 and sample standard deviation s = 5.8.

(a) Compute 90%, 95%, and 99% confidence intervals for ? using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

	90%	95%	99%
lower limit
upper limit

(b) Compute 90%, 95%, and 99% confidence intervals for ? using Method 2 with the standard normal distribution. Use s as an estimate for ?. Round endpoints to two digits after the decimal.

	90%	95%	99%
lower limit
upper limit

(c) Now consider a sample size of 81. Compute 90%, 95%, and 99% confidence intervals for ? using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

	90%	95%	99%
lower limit
upper limit

Compute 90%, 95%, and 99% confidence intervals for ? using Method 2 with the standard normal distribution. Use s as an estimate for ?. Round endpoints to two digits after the decimal.

	90%	95%	99%
lower limit
upper limit

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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