5 step procedure for a hypothesis test ## Example: Quarters- The U.S. Department of Treasury claims the mean mass of a quarter is 5.670 grams.- A simple random sample (SRS) of 50 quarters has a mean mass of 5.652 grams and a standard deviation of 0.068 grams.- Test the claim that the mean mass of quarters in circulation is 5.670 grams at a significance level of α = 0.10.### ExplanationTo test the claim, a hypothesis test can be conducted. The null hypothesis (H0) would state that the mean mass is 5.670 grams, while the alternative hypothesis (H1) would suggest that the mean mass is different from 5.670 grams. The significance level (α = 0.10) indicates the probability of rejecting the null hypothesis when it is actually true.

Given thatStep 1:Null Hypothesis:Alternative Hypothesis:Step 2:Test statistic:Step 3:p value:df=n-1=50-1=49Excel function:Step 4:Decision Rule: If p-value ≤ α, then reject the null hypothesis.Step 5: Conclusion: The level of significance is α=0.05Here, p value is less than the level of significance.From the decision rule, reject the null hypothesis.The mean mass of quarters in circulation is not equal to 5.670.The mean mass of quarters in circulation is not equal to 5.670 at α= 0.10.

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The U.S. Dept. of Treasury claims the mean mass of a quarter is 5.670 g.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Question

5 step procedure for a hypothesis test

## Example: Quarters

- The U.S. Department of Treasury claims the mean mass of a quarter is 5.670 grams.
- A simple random sample (SRS) of 50 quarters has a mean mass of 5.652 grams and a standard deviation of 0.068 grams.
- Test the claim that the mean mass of quarters in circulation is 5.670 grams at a significance level of α = 0.10.

### Explanation

To test the claim, a hypothesis test can be conducted. The null hypothesis (H0) would state that the mean mass is 5.670 grams, while the alternative hypothesis (H1) would suggest that the mean mass is different from 5.670 grams. The significance level (α = 0.10) indicates the probability of rejecting the null hypothesis when it is actually true.

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5 step procedure for a hypothesis test (z test NOT t test)

**Example: Quarters**

- The U.S. Dept. of Treasury claims the mean mass of a quarter is 5.670 g.
- A simple random sample (SRS) of 50 quarters has a mean mass of 5.652 g and a standard deviation of 0.068 g.
- Test the claim that the mean mass of quarters in circulation is 5.670 g at a significance level \(\alpha = 0.10\).

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