Answer to Question #268475 in Statistics and Probability for Adona

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

The following null and alternative hypothesis is needed to be tested:

$H_{0}: \mu=98.6$

v s 

$H_{1}: \mu \neq 98.6$

the critical value for two tailed t test at 0.05 level of significance is 1.983.

rejection region:

$\mathrm{R}=\{\mathrm{t}:|\mathrm{t}|>1.983\}$

test statistic:

$\begin{aligned} &t=\frac{\bar{x}-\mu_{0}}{\frac{s}{\sqrt{n}}} \\ &t=\frac{98.2-98.60}{\frac{0.62}{\sqrt{106}}}=-6.642 \end{aligned}$

since, $|t|=6.642>1.983$ null hypothesis is rejected.

Conclusion:

it is concluded that null hypothesis is rejected therefore , we have enough evidence to conclude that mean body temperature is different from 98.60 .