A.) What is the critical value of t for a 99% confidence interval with df=16? B.

Question

A.) What is the critical value of t for a 99% confidence interval with df=16? B.) What is the critical value of t for a 98% confidence interval with df=89? C.) What is the p-value for t greater than/equal to 2.41 with 7 degrees of freedom? D.) What is the p-value for |t| greater than 1.95 with 29 degrees of freedom? Two-tail probability One-tail probability Confidence levels Table T d 6314 12706 31821 63657 4.604 3.707 Values of t 3.078 1.638 1.533 2132 3.182 2.776 3.143 3.499 1397 18e0 1.356 2131 2 921 1.740 1.325 175 -323 2518 2069 314 313 2048 2045 2042 2462 1.694 1.690 1684 45 1.301 16% 1.306 2 423 1303 1299 1676 2.009 1.293 2403 2678 2.390 1.992 2 643 1.200 1.288 1656 1.973 1966 1646 1962 2.330 2341 1.284 1.282 1000 2581 1000 Confidence levels 0.10 One-tail probability 0.05 0 025

Explanation / Answer

A.) What is the critical value of t for a 99% confidence interval with df=16?

From the t-distribution tables, we get:

P( -2.921< t16 < 2.921 ) = 0.99

Therefore the critical value here is 2.921

B.) What is the critical value of t for a 98% confidence interval with df=89?

P( -2.369 < t16 < 2.369 ) = 0.98

Therefore the critical value here is 2.369

C.) What is the p-value for t greater than/equal to 2.41 with 7 degrees of freedom?

Using EXCEL the probability here is computed as:

=1-T.DIST(2.41,7,TRUE)

The output here is 0.023387

Therefore 0.023387 is the required p-value here.

D.) What is the p-value for | t | greater than 1.95 with 29 degrees of freedom?

Here the p-value is computed as:

P( | t29 | > 1.95 ) = 2P( t29 > 1.95 ) = 2*(1 - P(t29 < 1.95 ) )

This is computed using the EXCEL function as:

=2*(1-t.dist(1.95,29,TRUE))

The output here is 0.060903

Therefore 0.060903 is the required p-value here.

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