Parameters of a population include the mean, the standard deviation, the median or a proportion. Comparing two means from two separate populations might be our first task.

The study of identical twins

In the social sciences one of the best ways to study human parameters is through the use of identical twins. Since identical twins are genetically very similar scientists study them to decrease a lot of the variation between these twins and allow them to concentrate on non-biological variables.

In other words, studies recognize that twins are often the same height, the same weight, have a very similar IQ and so on. Therefore if the identical twins were raised by separate families (as sometimes happens) then does the economic status of their up-bringing effect their economic status later on? This would be a very good comparison of two parameters. Does the mean of the "poorer" brought-up twins equal the mean of the "richer" raised twins?

Clinical Trials

Clinical drug trials can be some of the most expensive undertakings. Patients or volunteers are in two or more separate groups and administered a new pharmaceutical or a placebo over an extended period of time. The results may compare one or more parameter and can obviously make a drug company if it is successful.

In the United States and Canada there are usually three phases of new drug testing. The first phase consists solely of prescribing the new drug to normally healthy individuals to see if there are side effects. Then there are still two more lengthy phases both of which involve many patients, hospitals and health care specialists.

Next, find the mean of the differences (d). Easy, points difference.

Find the standard deviation of the differences (d). points

Question

Use the data above concerning the two tests for those 6 individuals .

The means of two samples are compared where there is an implied dependency. Typically, the same person is involved in a "before" study and then with an "after" study".

Leonard Maltin's Movie and Video Guide provides us with movie lengths and other information.

Sample of TV Movies (lengths):

100 100 100 100 100 100 110 100 73 100
150 100 100 100 200 100 109 104 90 100
90 100 150 100 100 100 100 150 100 100
100

Sample of Cinema Movies (lengths):

104 101 109 101 119 100 96 95 106 145
94 102 118 87 119 117 97 111 100 100
105 102 108 240 100 109 101 100 91 101

Test at the 95% confidence level that the mean TV movie length is less than the mean cinema movie length. Test µ₁ < µ₂