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
c) identify the appropriate significance level.
d) calculate your test statistic. write the result below, and be sure to round your final answer to two decimal places.
e) calculate your p - value. write the result below, and be sure to round your final answer to four decimal places.

Explanation:

Part a)

Step1: Define Null Hypothesis ($H_0$)

The null hypothesis is the claim we are testing against, which is the commonly believed mean body temperature. So, $H_0: \mu = 98.6$ (where $\mu$ is the population mean body temperature).

Step2: Define Alternative Hypothesis ($H_1$)

The alternative hypothesis is the claim we believe, that the mean is not 98.6. So, $H_1: \mu
eq 98.6$.

Step1: Analyze the Alternative Hypothesis

The alternative hypothesis $H_1: \mu
eq 98.6$ means we are testing if the mean is either less than or greater than 98.6. This is a two - tailed test because we are interested in deviations in both directions (left and right) from the null hypothesis mean.

Step1: Recall the Significance Level

The problem states to use a 0.05 significance level. So, the appropriate significance level $\alpha=0.05$.

Answer:

$H_0: \boldsymbol{\mu = 98.6}$, $H_1: \boldsymbol{\mu
eq 98.6}$

Part b)