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# Free response example: Significance test for a mean

AP Statistics free response on significance test for a mean.

## Want to join the conversation?

• Is it possible to calculate the P-Value without the use of technology?
• I do believe the H0 should be < 128 as the problem mentioned the status que is at least 128 - what do you think ?
• "At least 128" means 128 or more (e.g. 129, 130...)
• If they fail and add more milk, that wouldn’t be coinsidered not with the regulations? meaning that Ha = mu != 128? Double tail?
• how can we calculate the P-value from the t-statistic manually without a TI-83.
• By using a t table. There is a video on KA that shows how to do that.
• Would this video also help with preparation for the 2021 AP stats exam?
I assume yes but want to check
• In the question, it states that the mean number of fluid ounces of milk in the containers is at least 128, but why the null hypothesis is mu=128? And why we can conclude that the alternative hypothesis is that mu is smaller than 128?
• The sample mean is below the minimum requirement of 128 fl.oz., which makes us suspect that the population mean is also below the minimum requirement (i.e., 𝜇 < 128), and that is what we're testing for.
• Is it possible to calculate the P-Value without the use of technology?
• Is it not P(t < t-value | (given that) mu = 128)?

Also, why is it assumed that alpha is .05?