Question

A 2014 study by the reputable Gallup organization estimates that 44% of U.S. adults are underemployed. Underemployed means the person wants to work full time but is employed part time or unemployed. We want to know if the proportion is smaller this year. We select a random sample of 100 U.S. adults this year and find that 40% are underemployed. After carrying out the hypothesis test for p = 0.44 compared to p < 0.44, we obtain a P?value of 0.21. Which of the following interpretations of the P?value is correct?

A. There is a 21% chance that 44% of U.S. adults are underemployed this year

B. There is a 21% chance that 40% of U.S. adults are underemployed this year.

C. There is a 21% chance that 40% or fewer U.S. adults are underemployed this year if 44% were underemployed in 2014.

D. There is a 21% chance that a sample of 100 U.S. adults will have 40% or fewer underemployed if 44% of the population is underemployed this year.

Answer 1

Option D - There is a 21% chance that a sample of 100 U.S. adults will have 40% or fewer underemployed if 44% of the population is underemployed this year.

Answer 2

Option A is right

Explanation:

Given that a 2014 study by the reputable Gallup organization estimates that 44% of U.S. adults are underemployed.

To check whether this proportion is smaller a hypothesis test conducted for a sample of 100 and sample proportion was found to be 0.40

p value =0.21

Normally p value is small, we reject null hypothesis. and if p is greater than alpha we accept null hypothesis

A. There is a 21% chance that 44% of U.S. adults are underemployed this year

is the right option.

Though hypothesis done for sample means, the interest was for the whole population.