A psychologist claims he has a test that predicts at age 5 what your annual inco

Question

A psychologist claims he has a test that predicts at age 5 what your annual income will be when you're 30, ± $8,000. He's administered the test to over 1,000 five-year-olds, and so far over 50 of them have reached 30 years of age. Of those 50 people, test results were accurate (within the specified range) for 40. Is this an impressive record? Why or why not? How would you go about calculating a P-value for this record, what kind of data would you need to calculate the value, and how low a P-value would you need to reject the hypothesis that the record of successful predictions was due to chance alone?

Explanation / Answer

According to the above data out of 50 ,40 people make the psychologists claim.It means 80% of the sample data are in confirmation with the annual income prediction.

Considering the average annual income of the population be X.Then the annual income is expected to lie within the range of +- $8000.

The data required would be the proportion of individual satisfying the prediction claim sampled randomly in a group of 50

The record is impressive or not depends on the significance level chosen because the claim is dependent on the hypothesis testing on the given significace level.

Considering let say psychologists said that the result is impressive only when the proportion that satisfied is greeater than 75%.So there the null and alternative hypothesis would be

H0:p=0.75

Ha:p>0.75

Thus,based on the above information and population size of 1000.The p-value is 0.8 .A z-test for proportion can be used to determine statistically whether the result is in cofirmation with the above value.

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