Question

it is commonly believed that the mean body temperature of a healthy adult is 98.6°f with a standard
deviation of 0.9°f. you are not entirely convinced. you believe that it is not 98.6°f. you collected data
using 39 healthy people and found that they had a mean body temperature of 98.97°f. use a 0.05
significance level to test the claim that the mean body temperature of a healthy adult is not 98.6°f.
a) identify the null and alternative hypotheses:
( h _ { 0 } : )
( h _ { 1 } : )
b) what type of hypothesis test should you conduct (left, right, or two - tailed)?
( \bigcirc ) left - tailed
( \bigcirc ) right - tailed
( \bigcirc ) two - tailed

Explanation:

Part a)

Step 1: Define Null Hypothesis ($H_0$)

The null hypothesis is a statement of no difference or the commonly accepted belief. Here, the commonly believed mean body temperature is $98.6^\circ F$. So, $H_0: \mu = 98.6$ (where $\mu$ is the population mean body temperature).

Step 2: Define Alternative Hypothesis ($H_1$)

The alternative hypothesis is what we are testing for. The claim is that the mean is not $98.6^\circ F$, so it's a two - tailed test for the alternative hypothesis. Thus, $H_1: \mu
eq 98.6$.

Part b)

The alternative hypothesis is $\mu
eq 98.6$, which means we are testing if the mean is either less than $98.6$ or greater than $98.6$. A two - tailed test is used when the alternative hypothesis has a "not equal to" sign, as we are interested in deviations in either direction from the null hypothesis value.

Answer:

s:
a) $H_0: \boldsymbol{\mu = 98.6}$, $H_1: \boldsymbol{\mu
eq 98.6}$
b) two - tailed