There are t critical values and there are t probabilities. Each requires knowledge of the sample size. The t distributio
Posted: Mon Jul 11, 2022 11:39 am
There are t critical values and there are t probabilities. Eachrequires knowledge of the sample size. The t distribution issymmetric just like the z distribution, just more spread out. Asthe sample size increases, the t distribution becomes more moundedand closer to the z distribution. Tables and technology take thesample size into consideration with df, where df = degrees offreedom = n − 1. The t probabilities are based on the t curve andt-values, just like the normal curve/probabilities are based onz-values. Table probabilities are often approximate and may begiven in interval form. Technology provides exact probabilities anduses cumulative probabilities. Note the direction ofinequalities.
Example: using technology, the exact probability can befound
P(t < −2.7, df = 15) = 0.008 P(t > 1.8, df = 29) =0.0411
Example: using a table, an interval for the probability can befound
P(t < −2.7, df = 15) gives (0.005, 0.01) P(t > 1.8, df =29) gives (0.025, 0.05) Part 1 of 3 Using a table or technology,find the following.
(i) P(t > −1.3, df = 10)
(ii) P(t < 1.6, df = 6)
Example: using technology, the exact probability can befound
P(t < −2.7, df = 15) = 0.008 P(t > 1.8, df = 29) =0.0411
Example: using a table, an interval for the probability can befound
P(t < −2.7, df = 15) gives (0.005, 0.01) P(t > 1.8, df =29) gives (0.025, 0.05) Part 1 of 3 Using a table or technology,find the following.
(i) P(t > −1.3, df = 10)
(ii) P(t < 1.6, df = 6)