Question

George is curious. He has been told that the average body temperature of humans is 98.6 degrees Fahrenheit. However, he believes it is much lower than that. He randomly selects 60 people from those passing by him on a street and takes their temperature. The average temperature of these 60 people is degrees Fahrenheit. The standard deviation, sigma_x, is known to be 0.62 degrees Fahrenheit. The p-value is less than 0.0001. What is the correct conclusion? Choose the correct answer below.

A. There is sufficient evidence that the average body temperature of the people in this study is less than 98.6 degrees Fahrenheit.
B. There is sufficient evidence that the average body temperature of all humans is less than 98.6 degrees Fahrenheit.
C. There is not sufficient evidence that the average body temperature of all humans is less than 98.6 degrees Fahrenheit.
D. There is sufficient evidence that the average body temperature of a humans is equal to 98.6 degrees Fahrenheit.

Answer 1

The correct option is (B).

Explanation:

In this case we need to test whether the average body temperature of humans is 98.6 degrees Fahrenheit.

The hypothesis can be defined as follows:

H₀: The average body temperature of humans is 98.6 degrees Fahrenheit, i.e. μ = 98.6.

Hₐ: The average body temperature of humans is less than 98.6 degrees Fahrenheit, i.e. μ < 98.6.

A random sample of n = 60 people are selected and their body temperatures are collected.

The population standard deviation is known to be, σ = 0.62.

As the population standard deviation is known, we will use the z-test for single mean.

The p-value of the test is, p-value = 0.0001.

We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.

Here the p-value is very low. So, the null hypothesis will be rejected at any significance level.

Thus, there is enough evidence to conclude that the average body temperature of humans is less than 98.6 degrees Fahrenheit.

Thus, the correct option is (B).