Question

We wish to check that normal body temperature may be less than 98.6 degrees. In a random sample of n = 18 individuals, the sample mean was found to be 98.217 and the standard deviation
was 0.684. Assume the population is normally distributed. Use=0.05.

Answer 1

Population standard deviation is unknown.

$H_0:\mu=98.6$

$H_a:\mu<98.6$

$t=\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}$

$t=\frac{98.217-98.6}{\frac{0.684}{\sqrt{18}}}$

$=-2.376$

$t_{0.05,17}=-1.74$

Since the test statistic -2.376 is less than the critical value -1.74, we reject the null hypothesis and conclude that there is enough evidence at 95% confidence level to conclude that normal body temperature is less than 98.6 degrees.