Question

1.   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

here we want to test,:  μ = 98.6 vs :  ≠ 98.6

the population standard deviation is unknown. so, we perform the one sample t test.

the test statistic T = which follows t distribution with df n-1 under the null hypothesis.

here the value of t statistic is T= -4.00

we reject at level 0.05, if  

= 2.0315

thus,

hence we reject the null hypothesis at 5 % level of significance

thus, 95% CI is given by (97.997, 98.403)