Question

Locate the value of t under the following conditions.

a. The sample size is 12 and the level of confidence is 95 percent
b. The sample size is 20 and the level of confidence is 90 percent.
c. The sample size is 8 and the level of confidence is 99 percent.

Answer 1

To determine the t-value for different confidence levels and sample sizes, one must use a t-table or statistical calculator, considering degrees of freedom (one less than sample size) and the desired confidence level.

Step-by-step explanation:

The value of t can be located using a t-table or a statistical calculator. When working with t-values, the degrees of freedom (df) are one less than the sample size (n - 1). The level of confidence represents the percentage of all possible samples that can be expected to include the true population parameter.

1. With a sample size of 12 and a 95% level of confidence, the df would be 12 - 1 = 11. Using a t-table or calculator, one would look up the value corresponding to a 95% two-tailed confidence interval and 11 degrees of freedom.
2. For a sample size of 20 and a 90% level of confidence, the df would be 19. The t-value for a 90% two-tailed confidence interval and 19 degrees of freedom needs to be located in the same manner.
3. With a sample size of 8 and a 99% level of confidence, the df would be 7. The corresponding t-value for a 99% two-tailed confidence interval and 7 degrees of freedom can be found.

Note that as the confidence level increases, the magnitude of the t-value also increases, meaning a wider interval for the same degree of freedom.