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 Choose one below: P < 0.005 P > 0.005 0.005 < P < 0.01 0.01 < P < 0.025
To estimate the P-value for a given one-mean t-test with a left-tailed test using a table of t-values, you need to locate the critical value for the given t-score and degrees of freedom (df = n - 1).
In this case, the t-score is -3.412 and the sample size is 12 (n = 12). The degrees of freedom will be df = 12 - 1 = 11.
To estimate the P-value, you will compare the t-score with the critical value obtained from the table of t-values.
First, locate the column for the degrees of freedom (df = 11) in the table of t-values. Then, scan down the column until you find the closest value to the given t-score (-3.412). Let's call this critical value t_critical.
Once you have the t_critical value from the table, compare it with the given t-score (-3.412). If the given t-score is smaller than or equal to the critical value, it means the P-value is smaller than or equal to the corresponding value from the table.
Considering the options provided:
- P < 0.005: If the P-value is smaller than 0.005, it means the t-score is even more extreme. This option seems unlikely since -3.412 is not extremely small.
- P > 0.005: If the P-value is greater than 0.005, it means the t-score is less extreme. This option seems more plausible since -3.412 is quite small.
- 0.005 < P < 0.01: This option suggests that the P-value falls between 0.005 and 0.01. We need to check if the given t-score falls within this range.
- 0.01 < P < 0.025: This option suggests that the P-value falls between 0.01 and 0.025. Again, we need to check if the given t-score falls within this range.
To determine which option is correct, you need to consult a table of t-values for the critical value t_critical corresponding to df = 11 and compare it with -3.412.
Unfortunately, without access to the specific table of t-values for df = 11, it is not possible to definitively choose between the given options. You would need to find a table that provides t-values for the specific degrees of freedom and check the value that corresponds to -3.412.
Once you have the t_critical value, you can compare it with the given t-score (-3.412) to determine the correct option.