Answered: The average life span in Ontario in…

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

The average life span in Ontario in 2009 was 81.3 years. A random sample of 17 obituaries from newspapers in Ontario showed ?¯x¯ = 82.5 and ?s = 2.6. If lifespan is assumed to be normally distributed, does this sample provide sufficient evidence to support that the average lifespan in Ontario has increased at the 1% significance level.

A. What are the null and alternative hypotheses?
(Type "mu" for the symbol ?μ, "xbar" for the symbol ?¯x¯, "p" for the symbol ?p, or "phat" for the symbol ?̂ p^, e.g. mu >> 0.5 for the mean is greater than 0.5, xbar << 0.5 for the sample mean is less than 0.5, p not = 0.5 for the proportion is not equal to 0.5, phat = 0.5 for the sample proportion is equal to 0.5.
Percentages should be provided as values between 0 and 1. Please do not include units.)
?0H0 :
??Ha :

B. What is the test statistic value? (Include as many decimals as possible.)
Test statistic =

C. What is the associated p-value? (Include as many decimals as possible.)
p-value =

D. Statistical decision:

A. There is evidence to support the alternative hypothesis at the 1% significance level and we would therefore accept the null hypothesis.
B. There is not enough evidence to support the alternative hypothesis at the 1% significance level and we would therefore fail to reject the null hypothesis.
C. There is not enough evidence to support the alternative hypothesis at the 1% significance level and we would therefore reject the alernative hypothesis.
D. There is not enough evidence to support the alternative hypothesis at the 5% significance level and we would therefore fail to reject the null hypothesis.
E. There is evidence to support the alternative hypothesis at the 1% significance level and we would therefore reject the null hypothesis.

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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