For the provided sample mean, sample size, and population standard deviation, complete parts (a) through (c) below. Assume that x is normally distributed. x=31 n=9 σ=6 a. Find a 95% confidence interval for the population mean. The 95% confidence interval is from _ to . (Round to two decimal places as needed.) b. Identify and interpret the margin of error. The margin of error is _ (Round to two decimal places as needed.) Interpret the margin of error. Choose the correct answer below. A. We can be 95% confident that the population mean, μ, is within the margin of error of the sample mean, 31. B. We can be 95% confident that any possible value of the variable is within the margin of error of the sample mean, 31. C. We can be 95% confident that any possible value of the variable is within the margin of error of the population mean, μ. D. We can be 95% confident that any possible sample mean is within the margin of error of 31. c. Express the endpoints of the confidence interval in terms of the point estimate and the margin of error. The 95% confidence interval is _______. (Round to two decimal places as needed.)

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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For the provided sample mean, sample size, and population standard deviation, complete parts (a) through (c) below. Assume that x is normally distributed.

x=31

n=9

σ=6

a. Find a 95% confidence interval for the population mean.

The 95% confidence interval is from _______ to __________.

(Round to two decimal places as needed.)

b. Identify and interpret the margin of error.

The margin of error is ___________

(Round to two decimal places as needed.)

Interpret the margin of error. Choose the correct answer below.

A. We can be 95% confident that the population mean, μ, is within the margin of error of the sample mean, 31.

B. We can be 95% confident that any possible value of the variable is within the margin of error of the sample mean, 31.

C. We can be 95% confident that any possible value of the variable is within the margin of error of the population mean, μ.

D. We can be 95% confident that any possible sample mean is within the margin of error of 31.

c. Express the endpoints of the confidence interval in terms of the point estimate and the margin of error.

The 95% confidence interval is _____________.

(Round to two decimal places as needed.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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