Sampling distribution

Question

Suppose research indicates that members of the millennial generation are continuing to be dependent on their parents into early adulthood. A family research organization claims that no more than 25% of individuals aged 18 to 34 continued to be dependent on their parents. Suppose a sample of 300 individuals aged 18 to 34 is selected and it is found that 100 of them continue to be dependent on their parents.

REQUIRED:

Conduct a hypothesis test to determine whether the proportion of millennials continuing to be dependent on their parents is higher than for past generations? Use the p-value approach.

Answer 1

H₀: p = 0.25 <--- p₀

H₁: p < 0.25

x = 100, n = 300 so p-hat = x / n = 100/300 = 0.333

z = (p-hat - p₀) / sqrt(p₀*(1-p₀)/n) = 3.3333

p-value = P(Z <= z) = P(Z <= 3.3333) = 0.9996

Thus there is not sufficient evidence to conclude that the population proportion is no more than 0.25, and the claim is not supported by the sample data. We fail to reject H₀.