# What Determines the Power of a Test in SAT Math Score Analysis?

• PrudensOptimus
To find the power of the test, we need to calculate the z-score for the given significance level and then use that value to find the corresponding probability from the standard normal table. This probability will be the power of the test against the alternative mu=500. In summary, the 5% significance level refers to the probability of rejecting the null hypothesis when it is true, and the power of the test against the alternative mu=500 is the probability of rejecting the null hypothesis at the 5% significance level when the alternative hypothesis is true.
PrudensOptimus
An SRS of 16 Orange County Schools' juniors had a mean SAT MATH of x = 500; and a Standard Deviation of s=100. We know that the population of SAT Math scores for juniors in the district is approximately normaly distributed. We wish to determine a 90% confidence interval for the mean SAT math score mu for the population of all juniors in the district.

Question: 1. For the SAT MATH Data above, find the power of the test against the alternative mu=500 at the 5percent significance level. Assume that Sigma=100.

How do I find the alternative? I know power... mu = 500... what is 5% significance level mean?

The 5% significance level refers to the probability of rejecting the null hypothesis (in this case, that the mean SAT Math score of juniors in the district is equal to 500) when it is true. The power of the test against the alternative mu=500 is the probability of rejecting the null hypothesis (at the 5% significance level) when the alternative hypothesis (that the mean SAT Math score of juniors in the district is not equal to 500) is true.

To find the power of the test against the alternative mu=500 at the 5% significance level, you will need to use a statistical software or calculator. The 5% significance level refers to the level of confidence in which we are willing to reject the null hypothesis. In this case, it means that we are 95% confident that the true mean SAT math score for all juniors in the district is within our calculated confidence interval.

To find the alternative, you will need to determine what you are comparing the mean SAT math score to. In this case, the alternative is mu=500, which means that we are interested in determining if the true mean SAT math score for all juniors in the district is equal to 500 or not.

Once you have the necessary information, you can use a statistical software or calculator to calculate the power of the test. This will give you an estimate of the probability of correctly rejecting the null hypothesis when the alternative is true.

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