Question

The marital status distribution of the U.S. male population, age 15 and older, is as shown below.

Marital Status	Percent
never married	31.3
married	56.1
widowed	2.5
divorced/separated	10.1

Suppose that a random sample of 400 U.S. young adult males, 18 to 24 years old, yielded the following frequency distribution. We are interested in whether this age group of males fits the distribution of the U.S. adult population at the 5% level. Calculate the frequency one would expect when surveying 400 people. Fill in the table below, rounding to two decimal places.

Marital Status	Frequency	What is the Expected Frequency
never married	137	?
married	240	?
widowed	3	?
divorced/separated	20	?

Part (a)

State the null hypothesis. Choose 1 or 2

1. The data fit the distribution of marital status for the U.S. adult population.

2. The data do not fit the distribution of marital status for the U.S. adult population.    

Part (b)

State the alternative hypothesis.

1. The data fit the distribution of marital status for the U.S. adult population.

2. The data do not fit the distribution of marital status for the U.S. adult population.    

Part (c)

What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)

________

Part (d)

State the distribution to use for the test.

t₃

?23

OR

t₄

?24

What is the Test STatistic?

What is the PValue?

Answer 1

null hypothesis: 1. The data fit the distribution of marital status for the U.S. adult population.

alternative hypothesis: 2. The data do not fit the distribution of marital status for the U.S. adult population.

c)

degrees of freedom =categories-1=4-1=3

d)?2₃

applying chi square test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
never married	0.313	137.000	125.20		1.112
married	0.561	240.000	224.40		1.084
widowed	0.025	3.000	10.00		4.900
dvorced/seperated	0.101	20.000	40.40		10.301
total	1	400	400		17.398

Test STatistic =17.398

p value =0.0006