A student wants to investigate the effects of real vs. substitute eggs on his favorite brownie recipe. He enlists the help of 10 friends and asks them to rank each of 8 batches on a scale from 1 to 10. Four of the batches were made with real eggs, four with substitute eggs. The judges tasted the brownies in random order. Here is a box plot of the data:

The mean score for the real eggs was 6.78 with a standard deviation of 0.651. The mean score for the substitute eggs was 4.66 with a standard deviation of 0.395.
a) What are the null and alternative hypotheses?
b) What do you conclude from the ANOVA table?
c) Do the assumptions for the test seem to be reasonable?
d) Perform a two-sample pooled f-test of the difference. What P-value do you get? Show that the square of the f-statistic is the same (to rounding error) as the F-ratio.

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3 6 4 Real Substitute Eggs ANOVA Table ANOVA Table Sum of Mean Source DF Squres Square F-Ratio P-Value Eggs 9010013 9.01001 31.0712 0.0014 Error 6 1.739875 0.28998 Total 7 10.749883