Some people claim that they can tell the difference between a diet soda and a re

Question

Some people claim that they can tell the difference between a diet soda and a regular soda in the first sip. A researcher wanting to test this claim randomly sampled 80 such people. He then filled 80 plain white cups with soda, half diet and half regular through random assignment, and asked each person to take one sip from their cup and identify the soda as diet or regular. 53 participants correctly identified the soda. (a) Do these data provide strong evidence that these people are able to detect the difference between diet and regular soda, in other words, are the results significantly better than just random guessing? (b) Interpret the p-value in this context. (c) Which type of error could have occurred in your hypothesis test?

Explanation / Answer

a) here as probabilty to guess it right through random guessing p=1/2

hence mean =np=80*0.5=40

and std deviation =(np(1-p))1/2 =4.472

hence detecting 53 or more right =P(X>=53)=1-P(Z<(52.5-40)/4.472)=1-P(Z<2.795)=1-0.9974 =0.0026

yes the result are significant; as p value is higher then 0.05.

b)p value represent probabilty of getting this result or more extreme value then this provided null hypothesis is true means each person is guessing.

c) as we are rejecting null ; hence type I error can occured, which happens when we reject null even it is true

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