Question

According to the U.S. Census Bureau, 69% of children under the age of 18 years in the United States lived with two parents in 2009. Suppose that in a recent sample of 2025 children, 1237 were living with two parents.

a. Using the critical value approach and α=0.1, test whether the current percentage of all children under the age of 18 years in the United States who live with two parents is different from 69%.

Round your answer for z to two decimal places.

z_observed =

z_{critical left} =

z_{critical right} =

b. How do you explain the Type I error in part a? What is the probability of making this error in part a?

P(Type I error) =E

c. Calculate the p-value for the test of part a. What is your conclusion if α=0.02?

Round your answer for the p-value to four decimal places.

p-value =

Answer 1

Null hypothesis, 0.69

Alternative Hypothesis, 0.69

pcap = 1237/2015 = 0.6139

Test statistic,

z = (0.6139 - 0.69)/sqrt(0.69*0.31/2015)
z = -7.39

Here the significance level, 0.1. This is two tailed test; hence rejection region lies to the both sides. = -1.64 and = 1.64

Reject H0 if test statistic, z < -1.64 or z > 1.64

z-observed = -7.39

z-critical(left) = -1.64

z-critical(right) = 1.64

b)

P(type I error) = alpha = 0.1

This is two tailed test,
p-value = 2*P(z < -7.39)
p-value = 0

as p-value < 0.02, reject H0
There is sufficient evidence to conclude that the current percentage of all children under the age of 18 years in the United States who live with two parents is different from 69%.