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 56 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 = □
(round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for the t - test statistic

The formula for the t - test statistic in a one - sample t - test is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(\mu\) is the population mean under the null hypothesis, \(s\) is the sample standard deviation, and \(n\) is the sample size.

Step2: Identify the values from the problem

We are given that \(\bar{x} = 98.3\), \(\mu=98.6\), \(s = 1\), and \(n = 250\).

Step3: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Answer:

\(-4.74\)