Chapter 8: Problem 12

Find the \(t\) value(s) for each of the following cases. a. Upper tail area of .025 with 12 degrees of freedom b. Lower tail area of .05 with 50 degrees of freedom c. Upper tail area of .01 with 30 degrees of freedom d. Where \(90 \%\) of the area falls between these two \(t\) values with 25 degrees of freedom e. Where \(95 \%\) of the area falls between these two \(t\) values with 45 degrees of freedom

Short Answer

Expert verified

a. \(t = 2.1788\) b. \(t = -1.6759\) c. \(t = 2.7500\) d. \(t = \pm 1.7081\) e. \(t = \pm 2.0141\)

Step by step solution

Case a: Upper tail area of .025 with 12 degrees of freedom

1. Refer to the t-distribution table, and look for the row titled "12" under the column "DF" (degrees of freedom). 2. Now, locate the column that has ".025" in the row "One Tail". This is the t value that corresponds to the upper tail area of .025 with 12 degrees of freedom. 3. Write down the t value.

Case b: Lower tail area of .05 with 50 degrees of freedom

1. Refer to the t-distribution table, and look for the row titled "50" under the column "DF" (degrees of freedom). 2. Now, locate the column that has ".05" in the row "One Tail". This is the t value that corresponds to the lower tail area of .05 with 50 degrees of freedom. 3. Write down the t value.

Case c: Upper tail area of .01 with 30 degrees of freedom

1. Refer to the t-distribution table, and look for the row titled "30" under the column "DF" (degrees of freedom). 2. Now, locate the column that has ".01" in the row "One Tail". This is the t value that corresponds to the upper tail area of .01 with 30 degrees of freedom. 3. Write down the t value.

Case d: Where 90% of the area falls between these two t values with 25 degrees of freedom

1. Refer to the t-distribution table, and look for the row titled "25" under the column "DF" (degrees of freedom). 2. Since 90% of the area falls between these two t values, there is a 5% chance in each tail. So, locate the column that has ".05" in the row "One Tail". This is the t value that corresponds to this case. 3. Write down the t value.

Case e: Where 95% of the area falls between these two t values with 45 degrees of freedom

1. Refer to the t-distribution table, and look for the row titled "45" under the column "DF" (degrees of freedom). 2. Since 95% of the area falls between these two t values, there is a 2.5% chance in each tail. So, locate the column that has ".025" in the row "One Tail". This is the t value that corresponds to this case. 3. Write down the t value.

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