Question

It has long been stated that the mean temperature of humans is

98.698.6degrees°F.

​However, two researchers currently involved in the subject thought that the mean temperature of humans is less than

98.698.6degrees°F.

They measured the temperatures of

4444

healthy adults 1 to 4 times daily for 3​ days, obtaining

200200

measurements. The sample data resulted in a sample mean of

98.398.3degrees°F

and a sample standard deviation of

0.90.9degrees°F.

Use the​ P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than

98.698.6degrees°F

at the

alphaαequals=0.010.01

level of significance.

State the hypotheses.

Upper H 0H0​:

muμ

equals=

98.698.6degrees°F

Upper H 1H1​:

muμ

less than<

98.698.6degrees°F

Find the test statistic.

t 0t0equals=nothing

Calculate the P

Should we reject this hypothesis and why?

Answer 1

To Test :-

H0 :- µ = 98.6
H1 :- µ < 98.6

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 98.3 - 98.6 ) / ( 0.9 / √(44) )
t = -2.2111

P - value = P ( t > 2.2111 ) = 0.0162 ( From t table )

Decision based on P value
Reject null hypothesis if P value < α = 0.01 level of significance
P - value = 0.0162 > 0.01, hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

No, since P value is greater than levle of signifiance, we should not reject null hypothesis.