About 90% of the general population is right-handed. A researcher speculates tha

Question

About 90% of the general population is right-handed. A researcher speculates that artists are less likely to be right-handed than the general population. In a random sample of 100 artists, 83 are right-handed. A student assistant was asked to interpret the meaning of the p-value in this situation. Their interpretation was that the p-value is the probability that the population of artists who are right-handed is less than 0.90, given that the sample proportion is 0.83. Do you agree or disagree? Explain using up to five sentences.

Explanation / Answer

Solution:

About 90% of the general population is right-handed.
A researcher speculates that artists are less likely to be right-handed than the general population.
In a random sample of 100 artists, 83 are right-handed. Which of the following best describes the p-value for this situation is

Ho: p = 0.9

Ha: p < 0.9 (implies a left-tail test)

p-hat = 0.83
z(0.83) = -2.3333
p-value = P(z<-2.333...) which is the P(prop. of rt.hand artists
is less than 0.83 if the population mean is 0.90)

The probability the sample proportion would be as small as 0.83, or even smaller, if the population proportion of artists who are right-handed is actually 0.90.

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