Question

a professor was interested in supernatural phenomenon and conducted an experiment to measure ESP( extra sensory perception). The professor asked a psychic to read his mind as he looked at pictures only he could see, and recorded the number of the correct descriptions given by the psychic. from this context, identify the null and the alternative hypothesis. why is the research appropriate for a binomial analysis.

Answer 1

The professor asked a psychic to read his mind as he looked at pictures only he could see and recorded the number of the correct descriptions given by the psychic.

Here, we would like to see the proportion of his correct predictions. We would like to see if it is more or less than a certain value. Suppose, here we are checking if it is less than 80%.

Null Hypothesis - p >= 0.8

Alternate Hypothesis - p < 0.8

It is appropriate for the binomial analysis as we use binomial when we need to calculate the probability/chances for some event successes in a particular number of attempts.

Bionomial distribution means the number of successes in a series of  n independent Bernoulli trials

And this is the similar case, number of successes that he predicts it right in n independent trials.