Answered: A random sample of 10 independent…

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

A random sample of 10 independent healthy people showed the body temperatures given below (in degrees Fahrenheit). Test the hypothesis that the population mean is not 98.6 F, using a significance level of 0.05.

98.3, 98.5, 99.0, 96.2, 98.4, 98.9, 97.8, 99.3, 98.7, 97.4

1. Find the test statistic. t = ____ (Round to two decimal places as needed.)

2. p-value = ____ (Round to three decimal places as needed.)

3. Interpret the results of the test.

A random sample of 10 independent healthy people showed the body temperatures given below (in degrees Fahrenheit). Test the hypothesis that the population mean is not 98.6 °F, using a significance level of 0.05.
98.3 98.5 99.0 96.2 98.4 98.9 97.8 99.3
98.7 97.4 O
Ha: H# 98.6
Ha: u = 98.6
Ha: µ< 98.6
Check the conditions to see whether the test statistic will follow a t-distribution.
The sample
random and the observations
independent. The distribution of the sample is
Find the test statistic.
t=
(Round to two decimal places as needed.)
Find the p-value.
p-value =
(Round to three decimal places as needed.)
Interpret the results of the test.
Since the p-value is
the significance level,
Ho- There is
v evidence to conclude that the population mean is not 98.6°F at a significance level of 0.05.

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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