Question

it has long been stated that the mean temperature of humans is 98.6°f. however, two researchers currently involved in the subject thought that the mean temperature of humans is less than 98.6°f. they measured the temperatures of 50 healthy adults 1 to 4 times daily for 3 days, obtaining 250 measurements. the sample data resulted in a sample mean of 98.3°f and a sample standard deviation of 1°f. use the p - value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than 98.6°f at the α = 0.01 level of significance.
state the hypotheses.
h₀: μ = 98.6°f
h₁: μ < 98.6°f
find the test statistic.
t₀ = - 4.74
(round to two decimal places as needed.)
the p - value is
(round to three decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 50\). So \(df=50-1 = 49\)

Step2: Find the P - value

Since this is a one - tailed \(t\) - test (\(H_1:\mu<98.6\)), and the test statistic \(t_0=-4.74\).
Using a \(t\) - distribution table or a calculator with a \(t\) - distribution function (e.g., in Excel: \(=\text{T.DIST}(t,df,1)\) where \(t=-4.74\), \(df = 49\), and the third argument \(1\) for a one - tailed test).
\(P-\text{value}\approx0.000\)

Answer:

\(0.000\)