Question

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 42 healthy adults 1 to 4 times daily for 3 days, obtaining 196 measurements. The sample data from those 196 measurements resulted in a sample mean of 98.4°F and a sample standard deviation of 0.9°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 e=0.05 level of significance. Click the icon to view the table of critical t-values State the null and alternative hypotheses. H H, VOF (Type integers or decimals. Do not round) Identify the test statistic. 1-(Round to two decimal places as needed.) Approximate the P-value The P-value is in the range Make a conclusion regarding the hypothesis. sufficient evidence to claim that the mean temperature of humans is the null hypothesis. There (Type an integer or a decimal. Do not round.)

Answer 1

null hypothesis: HO: μ		=	98.6
Alternate Hypothesis: Ha: μ		<	98.6

sample mean 'x̄=		98.400
sample size    n=		196
std deviation s=		0.9000
std error ='sx=s/√n=0.9/√196=		0.0643
t statistic ='(x̄-μ)/sx=(98.4-98.6)/0.064=		-3.11

p value      =

0.0011

from excel: tdist(3.111,195,1)

the p value is between 0.001 < p value <0.01

reject the null hypothesis,there is sufficient evidence,,,,,,,less than 98.6