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# Null and alternative hypothesis for t-test, state the decision

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Question #1- Using your experience from previous or current employment, provide a business example where you could use a t-test to assist in a business decision. State the null and alternative hypothesis. The null and alternative should be the exact opposite of each other and the t-test will be looking for a difference between two groups.

Here is an example: A business owner is looking to open a new location in addition to the six stores he already has open. He is curious if the stores located closer to the Interstate have a higher volume of customers on the weekend. He has 3 stores within 1 mile of an Interstate and 3 stores that are greater than 1 mile of an Interstate.

Null: The stores within 1 mile of an Interstate do not have a significantly different customer volume than the stores greater than 1 mile from an Interstate.

Alternative: The stores within 1 mile of an Interstate have a significantly different customer volume than the stores greater than 1 mile from an Interstate.

This would be a two-tailed test because I am just looking for a difference between the two groups. If I wanted to know if here was a higher volume, it would be a right tailed test and the wording of the hypothesis would change from significantly different to significantly higher.

Question #2- This is a continuation of the example you provided in Question #1. Provide the confidence level you would use for the example. (.01, .05, or .10)

Also, become familiar with the 5-step hypothesis testing method discussed in Chapter 9. How will you state your decision?

Example: The test statistic for this analysis exceeded the critical value, therefore we (accept/reject) the null. As a result, the business owner should...

Tip: Always provide the statistic first and then the business perspective.

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#### Solution Preview

1) Here is a situation where we ca use hypothesis testing at work. Imagine my company manufactures products. There is a high rate of errors in the manufacturing process, which is costing the company a lot of money. Management was wondering if implementing a new program, in which employees receive 4 extra hours of training, would reduce the number of errors that they make will decrease significantly, which would save the company money.

We could set up an experiment, with a hypothesis test.

What he would do is randomly assign xx employees to receive extra training, while xx employees are left status quo. Looking at historical data provided by the company, we know that on average, employees make xx mistakes per month. After the extra training is complete, we would examine their performance record, and see if the number of errors has decreased.

We would then be able to use hypothesis testing to statistically calculate if the experimental group made less errors.

We can set it up like this:

Null ...

#### Solution Summary

The null and alternative hypothesis for t-tests are examined. The expert states the decision.

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