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

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