find a t score (a) such that P( -a < t < a) = 0.95. Asume sample size n = 10.
To find the t-score that satisfies the given probability, you need to use the t-distribution table or a statistical calculator. Here's how you can do it step by step:
1. Determine the confidence level: The given probability, P(-a < t < a) = 0.95, refers to a 95% confidence level. This means that you want to find the t-score that corresponds to a 95% confidence interval.
2. Determine the degrees of freedom (df): In this case, the sample size is n = 10. For a sample size of 10, the degrees of freedom can be calculated as df = n - 1 = 10 - 1 = 9.
3. Find the critical value: The critical value corresponds to the t-score that splits the area under the t-distribution curve into two tails, each with an area of (1 - 0.95) / 2 = 0.025.
You can look up the critical value using a t-distribution table or use a statistical calculator. For example, using a t-distribution table, with a degrees of freedom (df) of 9 and a confidence level of 95%, the critical value corresponds to approximately 2.262.
The critical value is the t-score that represents the boundary where 2.5% of the values lie to the left and 2.5% lie to the right, leaving 95% in the middle.
4. Calculate the t-score (a): Since the t-distribution is symmetric around zero, you can simply take the negative of the critical value to get the lower t-score and the positive of the critical value to get the upper t-score.
Lower t-score: -2.262
Upper t-score: 2.262
Therefore, the desired t-score that satisfies the condition P(-a < t < a) = 0.95, with a sample size of 10, is -2.262 and 2.262.