Use a table of t-values to estimate the P-value for the specified one-mean t-test. Left-tailed test, n=12, t= -3.412. a=p<0.005. b= p>0.005. c= 0.005<p<0.01.
To estimate the P-value for the specified one-mean t-test, we need to use a table of t-values. The table will provide information about the critical values for different levels of significance, which we can then use to determine the P-value.
Here are the steps to estimate the P-value using a table of t-values:
Step 1: Determine the degrees of freedom (df)
For a one-mean t-test, the degrees of freedom (df) is equal to the sample size minus 1. In this case, n=12, so df=12-1=11.
Step 2: Identify the direction of the test
In this case, it is a left-tailed test. This means we are interested in determining if the t-value is significantly less than the mean.
Step 3: Determine the critical t-value
The critical t-value is the value that corresponds to the desired level of significance. In this case, we have three options:
a) a=p<0.005: If the desired level of significance is less than 0.005, we need to find the critical t-value that corresponds to a left-tailed test with alpha=0.005.
b) p>0.005: If the desired level of significance is greater than 0.005, we need to find the critical t-value that corresponds to a left-tailed test with alpha=0.005.
c) 0.005<p<0.01: If the desired level of significance is between 0.005 and 0.01, we need to find the critical t-value that corresponds to a left-tailed test with alpha=0.01.
Step 4: Locate the critical t-value in the table
To find the critical t-value in the table, locate the row corresponding to the degrees of freedom (df=11) and the column corresponding to the desired level of significance (as determined in Step 3).
Step 5: Determine the P-value
Once you have located the critical t-value in the table, compare it to the given t-value (-3.412) from the test. If the given t-value is more extreme (i.e., smaller) than the critical t-value, then the P-value is less than the desired level of significance. Otherwise, the P-value is greater than the desired level of significance.
So, to summarize your options:
a) If the critical t-value from the table is greater than -3.412, then the P-value is less than 0.005.
b) If the critical t-value from the table is less than -3.412, then the P-value is greater than 0.005.
c) If the critical t-value from the table falls between -3.412 and another value, then the P-value is between 0.005 and 0.01.
By following these steps, you can estimate the P-value for the specified one-mean t-test using a table of t-values.