Answer to Question #266801 in Statistics and Probability for needhelp

Question

1.   A sample of 106 body temperatures was found to have a mean of 98.20 and a standard deviation of 0.62.  Use a 0.05 significance level to test the claim that the mean body temperature of the population is equal to 98.6 as is commonly believed.  Is there sufficient evidence to conclude that the common belief is wrong?

Answer 1

Null hypothesis $H_0:\mu=98.6.$

Alternative hypothesis $Ha:\mu \ne 08.6.$

Test statistic: $t=\frac{98.20-98.6}{\frac{0.61}{\sqrt{106}}}=-6.64.$

Degrees of freedom: $df=106-1=105.$

P-value: $p=2P(T<-6.64)<0.0001.$

Since the p-value is less than 0.05, reject the null hypothesis.

There is a sufficient evidence to conclude that the common belief is wrong.