Question

A researcher claims that the average body mass index (BMI) of adult Canadians is more than 25.0. He takes a SRS of 250 Canadians and finds x = 26.3. The p-value for this test is 0.001. What is the best interpretation of this value?

Answer 1

Answer:

The probability of obtaining a result equivalent to or greater than what was the truly observed value of the test statistic is 0.001.

Step-by-step explanation:

The researcher can use a one sample z test to determine whether his claim is correct or not.

The hypothesis to test whether the mean BMI is more than 25.0, is defined as:

H₀: The mean BMI is not more than 25.0, i.e. μ ≤ 25.0.

Hₐ: The mean BMI is more than 25.0, i.e. μ > 25.0.

The test statistic is defined as:

$z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}$

The p-value of the test is,

p = 0.001.

The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or greater than what was the truly observed value of the test statistic.

A small p-value (typically ≤ 0.05) specifies sufficient proof against the null hypothesis (H₀), so you discard H₀. A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.

The p-value of 0.001 indicates that the probability of obtaining a result equivalent to or greater than what was the truly observed value of the test statistic is 0.001.

As the p-value is very small, the null hypothesis will be rejected at any level of significance.

Thus, concluding that the mean BMI of adult Canadians is more than 25.0.