It has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject thought that the mean temperature of humans is lessthan 98.6°F. They measured the temperatures of 61 healthy adults 1 to 4 times daily for 3 days, obtaining 275 measurements. The sample data resulted in a sample mean of 98.3°F anda sample standard deviation of 1.1°F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the o= 0.01 levelof significance. It has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject thought that the mean temperature of humans is lessthan 98.6°F. They measured the temperatures of 61 healthy adults 1 to 4 times daily for 3 days, obtaining 275 measurements. The sample data resulted in a sample mean of 98.3°F anda sample standard deviation of 1.1°F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the x = 0.01 levelof significance.State the hypotheses.Ho:H₁:98.6°F98.6°F

From given data we have : μ=98.6s=1.1n=275x¯=98.3H0 : mean = 98.6Ha : mean < 98.6Test statistic: t=x¯-μsn =98.3-98.61.1275 =-4.5227 p value is calculated using t= 4.5227, df = 275-1=274 at 0.01 significance level. P-value=0.000 [by excel =T.DIST(-4.5227,274,1)] Reject H0 since the P-value is less than the significance level.

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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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It has long been stated that the mean temperature of humans is 98.6°F. However, two researchers currently involved in the subject thought that the mean temperature of humans is less
than 98.6°F. They measured the temperatures of 61 healthy adults 1 to 4 times daily for 3 days, obtaining 275 measurements. The sample data resulted in a sample mean of 98.3°F and
a sample standard deviation of 1.1°F. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°F at the o= 0.01 level
of significance.

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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