Question

What percentage of the population live in their state of birth? According to the 2010 U.S. census, 14% of people born in Nevada, 26% of people born in Florida, 35% of people born in Virginia, 42% of people born in California, and 50% of people born in Arkansas live in that state. Suppose you wanted to see if these percentages still hold true today, so you randomly selected 40 people born in Arkansas and 22 said they live in that state. Based on your findings, can you conclude the proportion of all people born in Arkansas that live in that state is now lower at α=.025? For the hypothesis stated above, what is the decision rule? a. Reject H0 if the test statistic is less than -1.645. b. None of the answers is correct c. Reject H0 if the test statistic is less than -2.023. d. Reject H0 if the test statistic is less than -2.575. e. Reject H0 if the test statistic is less than -1.96.

Answer 1

p0 = 0.5, p=22/40=0.55, n=40, q=1-p=1-0.55=0.45

H0: p = 0.5, Proportion of all people born in Arkansas that live in that state is still the same

H0: p < 0.5, Proportion of all people born in Arkansas that live in that state is now lower

Test statistic, z = (p0-p)/(p*q*n)^0.5 = (0.5-0.55)/(0.55*0.45*40)^0.5 = -0.016

Tabulated z = z0.05 = 1.64

Since test statistic is less than 1.64, we do not reject null hypothesis and conclude that p = 0.5, Proportion of all people born in Arkansas that live in that state is still the same.

b. None of the answers is correct