HYPOTHESIS TESTING

 

Q1) A cinema hall has cold drinks fountain supplying Orange and Ditzy Colas. When the machine is turned on, it fills a 550ml cup with 500ml of the required drink. The manager has three problems.

I) The clients have been complaining that the machine supplies less than 500ml

II) The manager wants to make sure that the amount of cola does not exceed 500ml

III) The manager wants to minimize customer complaint and at the same time does not want any overflow.

He takes up 36 cups of sample and finds the sample mean to be 499 ml. The specification of the machine says that generally the standard deviation is 1 ml. He does a hypothesis testing at 10% level of significance.

Solution:

 1.What is the problem?

The clients have been complaining that the machine supplies less than 500ml and on other side  manager does not want any overflow. And wants to test it by statistical analysis whether our data supports what?

2.differentiate assumption and claim

Assumption= when the machine is turned on it fills upto 500ml of 550ml bottle.

Claim= but, clients are complaining about underfilling

3. formulate hypothesis

As clients are claiming about underfilling and also manager does not want any overfilling

Our alternate hypothesis-  :                                     

Null hypothesis -

(true mean of the population=  = mean volume of the cola’s filled.

Hypothesized mean= = given mean volume of the bottles.

Null hypothesis -

Our alternate hypothesis-  :

4. DETERMINE APPROPRIATE STATISTICAL TEST AND SAMPLING DISTRIBUTION

Two tailed test

Because clients are claiming for underfilling and manager cant afford overfilling.

Since σ is given we opt for z-distribution

5.SPECIFY SIGNIFICANCE LEVEL.

Probability of making type-1error = 10%

	Analytical conclusion			Action	Consequences
Assumption(null)	Reject	Type1 error	correct	rectify the machine.	Cost of maintenance
Claim(alternative)	Fail to reject	correct	Type2 error	No action	Dissatisfaction of customer.

 Type 2 error is more dangerous than type1.

5.calculate critical value and state the decision rule

If  Z > 1.96,  reject null hypothesis.

If  Z < -1.96, reject null hypothesis.

6.GATHER DATA

After deciding the hypothesis then decide the sampling method and then go for the survey and experimentation.

Sample size = n = 36

Sample mean =

Standard deviation of population= σ = 1ml.

7.CALCULATE THE OBSERVED VALUE.

Z test statistic =              

=

= -6

        -6             -1.96                 0                  +1.96

 

9.CONCLUSION

Since the test statistic is outside the nonrejection region and beyond the critical value

We reject the null hypothesis, that the  mean volume of the cola is 500ml

Our statistic analysis supports the research hypothesis and upholds the claim that mean volume of the cola is not 500ml.