Question

According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (USA TODAY, June 30, 2011). Suppose that in a recent sample of 1570 children, 239 were found to be living with at least one grandparent. At a 10% significance level, can you conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%? Use both the p-value and the critical-value approaches.

Round your answers for the observed value of z and the critival value of z to two decimal places, and the p-value to four decimal places.

z_observed =

p-value =

Critical value =

Answer 1

H0: p = 0.11

Ha: p > 0.11

Sample proportion = 239 / 1570 = 0.1522

test statistics

z = - p / sqrt( P (1 - p) / n)

= 0.1522 - 0.11 / sqrt ( 0.11 * 0.89 / 1570)

= 5.34

Critical z value = 1.282

p-value = P( Z > z)

= P( Z > 5.34)

= 0

Since test statistics > 1.282, we have sufficient evidence to reject h0,.

Since p-value < 0.10 level, we have sufficient evidence to reject H0.