describe an example of how we can use difference in populati

describe an example of how we can use difference in population means in hypothesis testing before making a business decision. Please give an independent sample example and paired (related) sample. explain your selection.

Solution

Independent Sample Example :

Suppose a distributor of bulbs was taking Bulb from company A which claimed that its bulbs has mean lifetime of 1465 hours. Now company B approaches the distributor and they claim that their bulbs live upto 1700 hours. The distributor is now in a limbo whether he should change the brand of bulbs or not. Even if he does change his brand will there be any valid reason behind it??? Or, the claim made by company B is just another gimmick.

So, he decides to test whether the average life time of bulbs from company B is higher than that of company A.

Here since both the manufacturers are different he can assume an indepence between lifetimes of two kinds of bulbs.

Here he applies a t test of mean differences to check whether the claim of company B is true(or at least their lifetime is higher than that of A).

If his test statistic gives a value within critical region he will conclude that lifetime of B\'s bulb are higher than that of A &subsequently will change his brand.

Paired Sample:

Suppose a company wants to introduce a new drug. But they are not quite sure whether this drug will overtake an existing drug as a pioneer of fever fighting drug in market. So they decide to test it\'s effectiveness. Their hypothesis was that this new drug is better than existing. They used the standard drug on a group of patients first & note down the avergae change of fever in the group. After one month cooling off period they used the new medicine on same group and note down the results.

Since the drugs were applied to same group of patients, the outcomes will be correlated somehow. So, it is better to use paired t test for mean difference,