If I test 50 people, I need 23 of them to pick the different beer for it to be considered statistically significant at 95% (or .05 risk which gives me a Chi-Squared Value of 3.841 to beat.) When I use my equation it works correctly from 15 correct responses and upward. When I tell it that there are less than 15 correct responses, it starts to increase the chi-squared value until around 8 people when it begins to say those are statistically significant answers which makes no sense.

Here is the equation (A22 is the total number of participants (50) and C22 is the number of correct responses (which should be 23 or higher to be significant):

=(((INT((A22-C22)-(A22*(2/3)))-0.5)^2)/(A22/3))+(((INT((A22-C22)-(A22*(2/3)))-0.5)^2)/(A22*(2/3)))

I tried to double check my work below and now this says that 23 people are not enough to be statistically significant (even though I found that number in a table in a math book.)

Outcome Class Observed outcomes Probability of each class Expected Occurances (obs-exp)2*/ exp

correct beer 23 0.333333333 16.66666667 2.406666667

wrong beers 27 0.666666667 33.33333333 1.203333333

Sum 50 1 50 3.61

3.61 is less than 3.84 yet the table says 23 people is the correct number for a sample of 50 participants...

Can someone please help me make sense of this? Sorry if it's an obvious answer...

Thank you for your help!

-Tony