Construct a 90% confidence interval, using the inequality . To test the effectiveness of a new drug that is reported to increase the number of hours of sleep patients get during the night, researchers randomly select 13 patients and record the number of hours of sleep each gets with and without the new drug.

The 90% confidence interval is (-1.987, -1.320).

Step-by-step explanation:

The data provided is:

Sleep without        Sleep using

    the drug           the drugd=without-with

         2.5                       4.3                  -1.8

         2.7                       4.2                  -1.5

         3.8                       5.0                  -1.2

         3.8                       6.2                 -2.4

          1.8                       2.5                 -0.7

         4.7                        7.1                 -2.4

         4.8                        7.1                 -2.3

         2.7                        3.3                 -0.6

         1.8                        3.5                 -1.7

        2.2                        4.3                 -2.1

        3.6                        4.3                 -0.7

        5.3                        7.0                  -1.7

        5.2                        7.6                 -2.4

Compute the sample mean and sample standard deviation:

The degrees of freedom of the test is:

df = n - 1 = 13 - 1 = 12

Compute the critical value of t for 90% confidence level and 12 degrees of freedom as follows:

Compute the 90% confidence interval as follows:

Thus, the 90% confidence interval is (-1.987, -1.320).

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.