two tailed test for experiment with N= 24. Can't find table of t critical
values, but tcv@ df=13. Compared tobt with tcv. Will this more likely create type I or type II error?
Using acronyms (e.g., tcv, bt) means nothing unless the acronym is defined. You are assuming that we use the same acronyms that you do, which in this case is not true. I can't answer unless I know what you are asking.
There should be a table of t values in the back of your statistics book.
df = n-1
To determine whether conducting a two-tailed test with N=24 and a t critical value (tcv) at df=13 is likely to create a type I or type II error, we need to understand the concept of each error type and the critical region.
1. Type I error: This is the error of rejecting a null hypothesis (H0) when it is, in fact, true. It represents a false positive, indicating that there is a significant effect when there might not be one.
2. Type II error: This is the error of failing to reject a null hypothesis (H0) when it is false. It represents a false negative, indicating that there is no significant effect when there might actually be one.
In a hypothesis test, the critical region (rejection region) is the area under the sampling distribution that, if the test statistic falls into it, leads to the rejection of the null hypothesis. The critical value (tcv) is the dividing point that separates the critical region from the non-critical region.
Now, let's apply this knowledge to your question. Since you mentioned that the t critical value (tcv) is available at df=13, we can assume that the t-distribution is being used for the test. Typically, the critical values at specific degrees of freedom (df) are found in a table of t critical values. However, since you mentioned that you cannot find the table, we'll take the tcv@df=13 as given.
To determine the likelihood of creating a type I or type II error, we need additional information:
1. The specific value of the calculated test statistic (tobt).
2. The actual values (mean, standard deviation) you are comparing with the null hypothesis.
With the above information, you can compare the tobt (test statistic) with the tcv (critical value) at df=13. Based on this comparison, you will either reject or fail to reject the null hypothesis.
If tobt falls into the critical region (tobt > tcv or tobt < -tcv), then the null hypothesis is rejected, leading to a potential type I error. This is because the null hypothesis is being rejected when it should not be.
On the other hand, if tobt does not fall into the critical region (|tobt| <= tcv), then the null hypothesis is not rejected, leading to a potential type II error. This is because the null hypothesis is not being rejected, despite it being false.
In summary, without the specific values of tobt and the comparison with the tcv, we cannot determine precisely which error is more likely to occur in your scenario. However, based on the typical interpretation of type I and type II errors, if tobt falls into the critical region and the null hypothesis is rejected, it is more likely to create a type I error.