# Ho Hypothesis

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How do I decide on formulas for Ho hypothesis?

The manager of a paint supply store wants to determine whether the amount of paint contained in 1 gallon cans purchased from a nationally known manufacturer actually averages 1 gallon. It is known from the manufacturer's specifications that the standard deviation of the amount of paint is equal to 0.02 gallons. A random sample of 50 cans is selected and the mean amount of paint per 1 gallon can is found to be 0.995 gallons.

State the null and alternative hypotheses

Is there evidence that the mean amount is different from 1.0 gall (use alpha =0.01)

Set up a 99% confidence interval estimate of the population average amount of paint.

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##### Solution Summary

The solution discusses how to decide on formulas for Ho hypothesis?

The manager of a paint supply store wants to determine whether the amount of paint contained in 1 gallon cans purchased from a nationally known manufacturer actually averages 1 gallon. It is known from the manufacturer's specifications that the standard deviation of the amount of paint is equal to 0.02 gallons. A random sample of 50 cans is selected and the mean amount of paint per 1 gallon can is found to be 0.995 gallons.

State the null and alternative hypotheses

Is there evidence that the mean amount is different from 1.0 gall (use alpha =0.01)

Set up a 99% confidence interval estimate of the population average amount of paint.

##### Solution Preview

As you know, there are two hypotheses - the null hypothesis. That is what everyone thinks is correct. In this case, the null hypothesis is that the cans have 1 gallon of paint. This is what is claimed.

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<br>Now, it may be that not all cans have 1 gallon of paint. Some may have less, some may have more. Therefore, the alternate hypothesis is that the cans of paint don't have 1 gallon in them

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<br>Ho: paint cans = 1 ...

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