Question

Suppose just over 2500 cell phones are produced at a factory today. Management would like to ensure that the phones' display screens meet their quality standards before shipping them to retail stores. Since it takes about 10 minutes to inspect an individual phone's display screen, managers decide to inspect a sample of 50 phones from the day's production.

(a) Explain why it would be difficult for managers to inspect an SRS of 50 phones produced today.

(b) An eager employee suggests that it would be easy to inspect the last 50 phones that were produced today. Obviously, this employee never took a stats class! Explain why this is not a good method.

(c) Another employee that did take a stats class recommends inspecting every 50th phone produced today. What sampling method are they using?

Answer 1

Solution:

A) The inspection of each phone display takes about 10 minutes. And also it's inspection cost seems to be expensive. Using proper sampling technique only we are able to check the quality. In the given problem they have adopted SRS method in SRS method there comes a choice between with replacement or without replacement . Here without replacement method should be followed therefore the probability of selection of second sample mobile is less compared to selection of first sample mobile.

Also the manager need to wait until the whole process is over and 2500 phones are put in a lot from that manager has to select 50 sample phone.

So it is difficult for the managers to inspect 50 phones display using SRS technique.

B) The employee suggested that it is easy to inspect last 50 phones. It is not an appropriate method of sampling . A sample should be the representative of population that is this 50 sample phone are representative of 2500 whole phones. If we select last 50 phones as sample then it won't give appropriate results , it can't be applied for whole population.

3) another employee who recommended inspecting the every 50th phone produced today suggested the Systematic Sampling technique. Because the production process is a continuous process and we don't want to wait untill whole process is over. We may select 50th phone , 100th phone ,150th phone ..... Etc

This 50th phone selection is because , we need 50 samples from 2500 phone

N/n = 2500/50 = 50

That's why the employee with stat knowledge have suggested this method.

And this is that appropriate method for selection of samples for this problem.