a random sample of 80 students at a large school shows an average grade of 72 in algebra with a standard deviation of 4. find the t-score you would use for an 95 % confidence interval
To find the t-score for a 95% confidence interval, you need two pieces of information: the confidence level (95%) and the degrees of freedom.
The degrees of freedom (df) for a one-sample t-test is n - 1, where n is the sample size. In this case, the sample size is 80, so the degrees of freedom would be 80 - 1 = 79.
Now, you can use a table, a statistical software, or a calculator that provides the t-distribution function to find the t-score corresponding to a 95% confidence level with 79 degrees of freedom. Here's how to find it using a calculator like Excel:
1. Open Excel and input "=T.INV.2T(1-Confidence Level, Degrees of Freedom)" into a cell. In this case, Confidence Level is 1-0.95 = 0.05 (because you want the 95% confidence level) and Degrees of Freedom is 79.
The formula in the cell should look like "=T.INV.2T(0.05, 79)".
2. Press Enter or Return, and the cell will display the t-score for the given confidence level and degrees of freedom.
For a 95% confidence interval with 79 degrees of freedom, the t-score would be approximately 1.990.