Answered: A recent article published in a medical…

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

A recent article published in a medical journal stated that the mean amount spent per person on prescription drugs in a recent year in the United States was about $460 with a standard deviation of $56. A random sample of 150 U.S. residents taken from the population found that the estimated mean amount spent per person on prescription drugs every year is $450.

(a)

Calculate the mean of the sampling distribution of the sample mean.

(b)

Calculate the standard deviation of the sampling distribution of the sample mean. (Round your answer to four decimal places.)

(d)

Calculate the probability of obtaining a sample result of a mean of $450 or more if the true population mean is 460. (Use a table or technology. Round your answer to four decimal places.)

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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