Answer to Question #119529 in Statistics and Probability for Putera

Question

a recent survey found that 68.6% of the population own their homes, In a random sample of 150 heads of households, 92 responded that they owned their homes. By using alpha = 0.01 does that suggest a difference from the national proportion

Answer 1

H₀:p=0.686

H₁:p≠0.686 (claim)

p=0.686, n=150, ṗ=92 /150=0.613

z=(ṗ-p)/$\sqrt{(p(1-p))/n}$ =(0.613-0.686)/$\sqrt{0.001436}$ =-1.918

p-value = (2)P(z < -1.918) = (2)(0.0276) = 0.0552 (two-tailed test)

Since p-value > 0.01, do NOT reject the null hypothesis. There is significant evidence that the mean proportion of homeowners is not different from 68.6%