Answered: It's proposed that the average life…

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

It's proposed that the average life expectancy these days is 53.5, but recent data suggests it might be more than that.

A sample size of 96 countries found a sample mean life expectancy of 59 years with a standard deviation of 13.9 years.

You want to formulate and test a hypothesis that can be used to challenge the validity of the claim at a significance level of 0.05.

With hypotheses H0:μ≤53.5 vs H1:μ>53.5, what is/are the critical value(s)? (Report answer accurate to 2 decimal places.)

What is the test statistic for this sample?
(Report answer accurate to 3 decimal places.)

What is the p-value for this sample?
(Report answer accurate to 4 decimal places.)

Our decision is to

reject the null
accept the null
fail to reject the null

As such, the final conclusion is that

there is sufficient evidence to conclude that the population mean life expectancy is equal to 53.5.
there is not sufficient evidence to conclude that the population mean life expectancy is equal to 53.5.
there is sufficient evidence to conclude that the population mean life expectancy is greater than 53.5.
there is not sufficient evidence to conclude that the population mean life expectancy is greater than 53.5.

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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