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=
Hypothesized mean=
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.
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