Question

Carl Reinhold August Wunderlich reported that the mean temperature of humans is 98.6F. To test this long-held belief about the average body temperature, medical researchers measured the temperature of 36 randomly selected healthy adults. The sample data resulted in a sample mean of 98.2F and a sample standard deviation of 0.6F. Assuming that the population is normal, test whether the mean temperature of humans is different from 98.6F at the 5% significance level. To gain full credit, you should provide the following


(a) State and check the modeling assumptions.

(b) Define the parameter of interest.


(c) State the hypotheses.

(d) Calculate the value of the test statistic. What is the distribution of the test statistic?


(e) Find the p-value using the appropriate table.

(f) State the decision and the conclusion in the context of the problem.


(g) Calculate a 95% confidence interval for the population mean µ and interpret your interval in the context of this problem.

(h) Could we have used the 95% confidence interval calculated in (g) to make a decision about the hypothesis test conducted? Discuss, in depth, why or why not this can be done.

Answer 1

(a) State and check the modeling assumptions.

To perform

sample should be simple random sample

sample should follow normal distribution

Given popualtion is normal,so sample which is taken from popualtion is normal

n=36, large sample sample follows noraml distribution

Given sample is 36 randomly selected healthy adults ,so it is a random sample

(b) Define the parameter of interest.

parameter of interest is population mean  temperature of humans

population mean denoted by mu

mu=98.6 F

(c) State the hypotheses.

Null hypothesis,Ho:

Alternative Hypothesis,Ha:

(d) Calculate the value of the test statistic. What is the distribution of the test statistic?

test statistic=t

t=xbar-mu/s/sqrt(n)

t=(98.2-98.6)/(0.6/sqrt(36))

t=-4

distribution of the test statistic is t distribution with n-1=36-1=35degrees of freedom

(e) Find the p-value using the appropriate table.

p value in excel

=T.DIST.2T(4,35)

=0.000312

p-value=0.000312

(f) State the decision and the conclusion in the context of the problem.

p<0.05

Reject Ho

Accept Ha

There is suffcient statistical evidence at 5% level of significance to conlcude that the mean temperature of humans is different from 98.6F