Question

A sports physician conducted a study to investigate whether there is an association between running experience and the occurrence of a certain sport injury for marathon runners while training for a marathon. Data were collected on a random sample of 51 marathon runners. Each runner from the sample was categorized by running experience (low, medium, high) and whether or not the runner experienced the sport injury while training for a marathon. The conditions for inference were met, and a χ2 test statistic of approximately 8.12 was calculated.

Which of the following describes the p-value of the test?


p-value>0.25

0.10
0.05
0.01
p-value<0.01

Answer 1

The p-value for a χ² test statistic of approximately 8.12 is likely between 0.05 and 0.01, as the exact p-value would require knowledge of the degrees of freedom which is not provided.

Step-by-step explanation:

When looking at the χ2 test statistic of approximately 8.12 that was calculated in a study to investigate whether there is an association between running experience and the occurrence of a sport injury for marathon runners, we have to compare the calculated test statistic with a χ2 distribution to find the p-value. The test provides the probability that the observed association between categories is due to chance alone. The significance level of the study, typically denoted as alpha (α), helps determine whether to reject the null hypothesis. A common alpha level used in such studies is 0.05. Comparing the test statistic to tables or software that provide the distribution of χ2 values, one can find the corresponding p-value.

Given that we do not have the specific degrees of freedom for this test, we cannot determine the exact p-value. However, the range it falls into can usually be ascertained. For instance, if the degrees of freedom were between 1 and 10 and using a standard χ2 distribution table, a test statistic of 8.12 typically corresponds to a p-value that is between 0.05 and 0.01. Without more information, we cannot be more specific than this.

Therefore, given the choices provided, the p-value for a χ2 test statistic of approximately 8.12 is most likely between 0.05 and 0.01.

Answer 2

D 0.01< p-value <.05

Step-by-step explanation:

since 8.12 is our test statistic, we only need to know the degrees of freedom to get our answer. if we were to make a chart of all the catagories we would get 3 rows(low, medium, high) and 2 columns (experienced sport injury while training, and not) In order to find our degrees of freedom we multiply our rows minus 1 and our columns minus 1.

so (3-1)(2-1) and we get 2.

so we can plug these numbers into a calculator and get a p value of .01725, which is in between .01 and .05. Therefore the answer is

D 0.01<p-value<.05