Question

Find a real world business example or examples in a case study and comment on the way hypothesis testing can be applied to answer a relevant business question. Identify the question(s) in your post and provide the data set at an attachment as a reference. Finally, explain how you would approach using the data set to answer the business question.

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Answer 1

1. Hypothesis testing is used in many business applications everyday. With the growing amount of data, it is vital for any business to use this data to their advantage. Hypothesis testing is used to help verify any assumption or a particular statement and take business decisions on the basis of it. In the process, at first, the particular statement or the hypothesis is assumed to be incorrect and then usin the data, statistical evidence is found to prove that the hypothesis is true or not. We can take an example of a very relevant business application which uses hypothesis testing:

There is a factory which manufactures widgets and they claim that their widget size is 5 mm, with just a small tolerance. Hence, the buyer needs to see that this claim is correct or not. Hence, the hypothesis will be:

Null Hypothesis: The widget size equals 5 mm
Alternate Hypothesis: The widget size does not equal 5 mm

The buyer collects a random sample of size = 30. He collects it from the daily data of the factory on a particular day. They need a very strict measurement, hence they take the confidence level or significance level as 1%.

First of all, the average and standard deviation is measured. The data is assumed to be normal. The data is given below:

Size (mm)

5.1 5.09 4.77 5.08 5.08 5.11 5.11 4.89 5.02 4.95 4.96 4.77 5.17 4.99 4.81 5.14 4.89 5.05 5.16 4.91 4.91 5.11 5.1 5.08 4.96 5.04 5.06 5.12 4.97 5.01

Average = 5.01
Standard deviation = 0.11

The buyer performs a one sample t-test to test the mean. He calculates the t-statistic:

t = (5.01 - 5)/0.02 = 0.01/0.02 = 0.50

The associated p-value with the t-statistic (df = 30 - 1 = 29) is 0.62 (from the t-table)

The p-value is not significant at 0.01 (as p>0.01) hence we cannot reject the null hypothesis. Therefore, the buyer takes the decision that the widget size is equal to 5 mm and he can trust the manufacturer.