Answer:
The t-score is 1.96
Step-by-step explanation:
The margin of error is given as
(Margin of Error) = (critical value) × (standard deviation of the sample mean)
The critical value is usually obtained from the t-score or the z-score at the given confidence level.
With small sample sizes (sample sizes less than 30) and/or information about the population standard deviation is not known, the t-distribution is used to find critical values.
We convert the confidence level to significance level and use the sample size to trace out the t-score.
Significance level = (1 - confidence level)/2
For example, a confidence level of 95% mean that 5% (spread equally at the top and bottom of the distribution as 2.5% and 2.5%) is still room for error, hence, the significance level = (5%/2) = 2.5%
This information, with the sample size, directs one exactly to where to obtain the t-score for the distribution on the t-score table.
But, with large sample sizes, with known information about its standard deviation, we typically use critical values on the Z-distribution to obtain the margin of error.
And as the sample size increases, the t-score approximates the z-score.
So, for a sample size of 100, the t-score can be simply obtained from the z-score table for a confidence level of 95%; and that is 1.96.
Hope this Helps!!!
