Testing of Hypothesis

One objective of sampling theory is Hypothesis Testing. Hypothesis testing begins by making an assumption about the population parameter. Then we gather sample data and determine the sample statistic. To test the validity of our hypothesis the difference between the hypothesized value and the actual value of the sample statistic will be determined. If the difference between the hypothesized population parameter and the actual value is large then we automatically reject our hypothesis. If it is small, we accept it.

Example 

A cinema hall has a cool drinks fountain supplying Orange and Ditzy Colas. When the machine is turned on, it fills a 550 ml cup with 500 ml of the required drink.

The manager has two problems on hand.

1. The clients have been complaining that the machine supplies less than 500 ml.

2. The two colas are supplied by two different manufacturers, each pressurizing him to drop the other supplier. Should he drop one?

On a particular day, he took a survey of the clients. There were n clients. The percentage of clients asking for Ditzy was     . The rest     , took Orange (    +      = 1). Moreover, the average volume of liquid in the cups was      ml.

(The values of      and      will be given later.)

How can we help him to solve the problems?