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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!!!
For the sample size 100, the value of the t-score is 1.96 and this can be determined by using the given data.
Given :
- A sample of 100 information systems managers had an average hourly income of $40.00 with a standard deviation of $8.00.
- 95% confidence interval.
The following steps can be used in order to determine the value of t:
Step 1 - First, determine the z-score for 95% confidence interval.
z = 1.96 for 95% confidence interval.
Step 2 - For the larger sample size, the z-score and t-score are approximately the same.
Step 3 - So, for 100 sample size which is larger, the t-score is equal to 1.96.
For more information, refer to the link given below:
https://brainly.com/question/25677563
