Answered: You are interested in estimating the…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

You are interested in estimating the mean of a population. You plan to take a random sample from the population and use the sample’s mean as an estimate of the population mean.

Assuming that the population from which you select your sample is normal, which of the statements about M are true? Check all that apply.

You can only assume that the sampling distribution of M is normally distributed for sufficiently large sample sizes.

You can assume that the sampling distribution of M is normally distributed for any sample size.

The standard deviation of the sampling distribution of M is equal to the standard deviation of the population divided by the square root of the sample size.

The expected value of the sampling distribution of M is equal to the value of the population mean divided by the sample size.

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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