A random sample of 20 recent weddings in a country yielded a mean wedding cost of $26,396.48. Assume that recent wedding costs in this country are normally distributed with a standard deviation of $7900. a. The 95% confidence interval is from $ to $ _ b. Interpret result We can be 95% confident that the sample cost of recent weddings in this country is somewhere within the confidence interval. We can be 95% confident that any randomly selected recent wedding cost in this country is somewhere within the confidence interval. The mean cost, μ,of all recent weddings in this country is somewhere within the confidence interval. We can be 95% confident that the mean cost, μ,of all recent weddings in this country is somewhere within the confidence interval. c. Does the mean cost of all recent weddings in this country lie in the confidence interval obtained in part (a)? The sample mean may or may not lie in this interval, but we can be 95% confident that it does. The population mean may or may not lie in this interval, but we can be 95% confident that it does. No, since there is a 5% chance that the population mean does not lie in the confidence interval. Yes, since the confidence interval must contain the sample and population means.

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

A random sample of 20 recent weddings in a country yielded a mean wedding cost of

$26,396.48.

Assume that recent wedding costs in this country are normally distributed with a standard deviation of $7900.

a. The 95% confidence interval is from

$____ to $ _____

b. Interpret result

We can be 95% confident that the sample cost of recent weddings in this country is somewhere within the confidence interval.

We can be 95% confident that any randomly selected recent wedding cost in this country is somewhere within the confidence interval.

The mean cost, μ,of all recent weddings in this country is somewhere within the confidence interval.

We can be 95% confident that the mean cost, μ,of all recent weddings in this country is somewhere within the confidence interval.

c. Does the mean cost of all recent weddings in this country lie in the confidence interval obtained in part (a)?

The sample mean may or may not lie in this interval, but we can be 95% confident that it does.

The population mean may or may not lie in this interval, but we can be 95% confident that it does.

No, since there is a 5% chance that the population mean does not lie in the confidence interval.

Yes, since the confidence interval must contain the sample and population means.

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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