If a study yields a p pvalue 05 alpha 05 is the standard

If a study yields a p<.05, what interpretation can be made?

Solution

p < .05

--> p-value < .05

--> alpha = .05 is the standard level of significance used in hypothesis testing

--> Whenever the p-value < or = alpha, we reject Ho

--> p-value < .05 means we can reject Ho for all values of alpha .05 or larger

--> So, if alpha = .05 (or .06, .10, etc.), we can reject Ho and conclude Ha

--> So, our results are \"statistically significant\", i.e. our results were NOT likely to happen by chance

--> More specifically, there is less than 1 chance in 20 (1/20 = .05) that we observed sample data equal to or more extreme than what we did assuming Ho is true

--> based on the sample data we have sufficient evidence to BELIEVE Ha is true (but, we did NOT prove Ha is true; we DON\'T prove anything in stats)

For example... Suppose we want to test whether a beer bottling machince is out of calibration. If the machine is properly calibrated it should dispense on average 12.2 oz. of beer with a standard deviation of .1 oz. Suppose a random sample of 16 bottles of beer produced a sample mean of 12.2625 oz. Can we conclude that the beer bottling machine is overfilling the bottles of beer? Test using a .05 level of significance.

Ho: mu = 12.2 vs. Ha: mu > 12.2

Since sigma = the population standard deviation is known, use z...
z = (12.2625-12.2)/(.1/sqrt(16) = 2.5

p-value
= P(xbar > or = 12.2625 if mu = 12.2)
= P(Z > or = 2.5)
= .0062

Is p-value < or alpha?
Is .0062 < or = .05?
Yes, so reject Ho and conclude Ha
So, based on the sample data, we CAN conclude that mu > 12.2, i.e. we can conclude that the machine is overfilling the bottles of beer.

So, since p-value < .05...
* our results are statistically significant
* our sample data wasn\'t likely to occurred by chance
* it is unlikely that we observed a sample mean of 12.2625 or more if mu really equals 12.2
* based on the sample data Ha is true, i.e. mu > 12.2

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I hope this helped. If you have any questions, please ask them in the comment section. :)