Answered: A government initiative is implemented…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section: Chapter Questions

Problem 8SGR

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Question

A government initiative is implemented to reduce the average annual out-of-pocket medical costs for senior citizens. It is known from previous data that under the old system, the population mean annual cost was $5340 and the population standard deviation was $2010. After the new program is implemented, the annual out-of-pocket medical costs are recorded for a sample of 75 senior citizens, and the resulting sample mean is $4820.

a. Construct the 99% confidence interval for the new population mean, assuming the population standard deviation remains unchanged.

Point Estimate =

Standard error=

Z=±

99% confidence interval is

Does the result seem to support the government's claim that the new program has reduced the annual out-of-pocket cost to seniors?

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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