Find a t score (a) such that P( -a < t < a) = 0.95. Asume sample size n = 10.
To find the t-score, we need to use a t-distribution table or a statistical calculator. In this case, we want to find the value of "a" such that the probability of getting a t-score between -a and a is 0.95.
First, let's determine the degrees of freedom (df). For a sample size of n = 10, the degrees of freedom for a t-distribution is calculated as df = n - 1 = 10 - 1 = 9.
Next, we can use the cumulative probability values of the t-distribution table to find the corresponding t-scores. In this case, we want the probability to be 0.95, which means we need to find the t-scores that enclose 95% of the area under the curve.
Since the t-distribution is symmetric, we can divide the probability (0.95) by 2 to find the area in each tail. Thus, we are looking for a value that corresponds to a cumulative probability of (1 - 0.95)/2 = 0.025 in each tail.
Using a t-distribution table or a statistical calculator, we find that for a degrees of freedom (df) of 9, the t-score that corresponds to a cumulative probability of 0.025 in each tail is approximately 2.2622.
Therefore, the t-score we are looking for (a) is approximately 2.2622. This means that the probability of getting a t-score between -2.2622 and 2.2622 is 0.95 for a sample size of 10.