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 1610 children, 234 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. zobserved =Enter you answer; z_observed p-value =Enter you answer; p-value Critical value =Enter you answer; Critical value We can conclude that the proportion of all children in the U.S. who currently live with at least one grandparent is Choose the answer from the menu in accordance to the question statement11%.

Answer 1

Null Hypothesis, 0.11

Alternative Hypothesis,   0.11

pcap = 234/1610 = 0.1453

Test statistic,

z = (0.1453 - 0.11)/sqrt(0.11*0.89/1610)
z = 4.53

This is right tailed test,
p-value = P(z > 4.53)
p-value = 0.0000

Here the significance level, 0.1. This is right tailed test; hence rejection region lies to the right. 1.28 i.e. P(z > 1.28) = 0.1

Reject H0 if test statistic, z > 1.28

Reject H0

there is significant evidence to conclude that more than 11% of of all children in the United States who currently live with at least one grandparent