Dr. Richards examined which cereal people liked better: Cocoa Puffs or Rice Kris

Question

Dr. Richards examined which cereal people liked better: Cocoa Puffs or Rice Krispies.

A total of 20 participants were recruited. The 20 people were randomly assigned to eat one cereal or the other (half rated one cereal and half rated the other).

Cocoa Puffs got an average rating of 7.8 on a 10 point scale. But Rice Krispies only got an average rating of 5.2. This is a statistically significant difference at the alpha level of .05.

The value of t-obtained was 3.674 according to the hand calculations Dr. Richards performed.

Write a complete conclusion in APA style, which includes both an explanation in words and a statement of the statistical results.

Continuing with Dr. Richards experiment about whether people preferred Cocoa Puffs or Rice Krispies, recall that two independent groups of participants the cereals on a 10 point scale. Now you are being told that r2=.4280 so write a conclusion describing what this result means.

Explanation / Answer

We state the null and alternate hypothesis as below:-

H0: 1 - 2 = 0 i.e. (1 = 2)

H1: 1 - 2 0 i.e. (1 2)

degrees of freedom is (20-2)=18 and with 0.05 alpha level, we get the critical value of t to be 2.1009. The value of t-obtained is 3.674 and hence it falls in the rejection region (3.674>2.1009). Therefore, the conclusion is There is evidence of a difference in means.

Here, we see that r^2=0.4280 which means that around 43% of the variation in dependent variable is due to the independent variables in the model. Here the independent variables are independent groups of participants.

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