Question

Runaways The FBI has stated that most runaways are females. A recent sampling of 90 cases involving runaways indicated that 63 of them were female.

a. What is the inherent question of interest here?

b.What might be a reasonable description of the population of interest?

c.What is the relevant sample here?

d.What is the random variable being evaluated here?

e.What is the population parameter of interest?

f.What is this parameter’s corresponding sample statistic?

g.What is an appropriate research hypothesis to consider?

h.What is the corresponding null hypothesis?

i.What is the test statistic used to test these hypotheses?

j.What is the null distribution of this test statistic?

k.What is the decision rule that might be used here?

l.What decision was made with regard to the null hypothesis?

m.What is your conclusion based on the available data?

Answer 1

(a)

The inherent question of interest here is: Are most runaways females?

because it is given: The FBI has stated that most runaways are females. In this hypothesis test, we are testing whether this is true.

(b)

A reasonable description of the population of interest is: All persons who have runaway.

because we are testing whether most runaways are females.

(c)

The relevant sample here : 90 cases involving runaways

because it is given: A recent sampling of 90 cases involving runaways indicated that 63 of them were female.

(d)

The random variable being evaluated here: The proportion of females in runaways.

(e)

The population parameter of interest : The proportion of females in the entire runaways.

(f)

This parameter’s corresponding sample statistic The proportion of females in the sample of 90 cases of runaways.

(g)

An appropriate research hypothesis to consider :
H1: P > 0.50 (The most runaways are females)

(h)

The corresponding null hypothesis :

H0: P 0.50 (The most runaways are not females)

(i)

the test statistic used to test these hypotheses:

Z test for one population proportion

(j)

the null distribution of this test statistic :

Standard Normal Distribution

(k)

the decision rule that might be used here:

Since Significance Level = is not provided,

Take = 0.05

From Table, critical value of Z = 1.64

Decision Rule:
Reject H0 if Z > 1.64

(l)

Test Statistic is given by:

Since calculated value of Z = 3.795 is greater than critical alueof Z = 1.64:

The decision that was made with regard to the null hypothesis

reject null hypothesis.

(m)

Conclusion:

The data support the claim that the most runaways are females.