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	Expected Frequency
never married	136
married	240
widowed	2
divorced/separated	22

Part (a)

State the null hypothesis. Choose 1 or 2

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

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

State the alternative hypothesis. Choose 1 or 2

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

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

Part (b)

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

_______________

Part (c)

State the distribution to use for the test. Choose 1 2 3 4

1. ?24

2. t₄

3. ?23

4. t₃

Part (d)

What is the test statistic? (Round your answer to two decimal places.)

__________

What is the p-value? (Round your answer to four decimal places.)
____________
Explain what the p-value means for this problem. CHoose 1 2 3 or 4

1. If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.

2. If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.    If

3. H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.If

4. H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.

part (e)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write the appropriate conclusion.

(ii) Decision: Choose 1or 2

1. reject the null hypothesis

2. do not reject the null hypothesis    

(iii) Reason for decision: Choose 1 2 3 4

Since ? < p-value, we do not reject the null hypothesis.

Since ? > p-value, we do not reject the null hypothesis.    

Since ? > p-value, we reject the null hypothesis.

Since ? < p-value, we reject the null hypothesis.

(iv) Conclusion: Choose 1 or 2

1. There is sufficient evidence to conclude that the data do not fit the distribution of marital status for the U.S. adult population.

2. There is not sufficient evidence to conclude that the data do not fit the distribution of marital status for the U.S. adult population.   

Answer 1

applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
never married	0.313	136.000	125.20		0.932
married	0.561	240.000	224.40		1.084
widowed	0.025	2.000	10.00		6.400
divorced	0.101	22.000	40.40		8.380
total	1	400	400		16.796

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
never married	0.313	136.000	125.20		0.932
married	0.561	240.000	224.40		1.084
widowed	0.025	2.000	10.00		6.400
divorced	0.101	22.000	40.40		8.380
total	1	400	400		16.796

expected frequency is given on above table:

a)

null hypothesis: 2. The data fit the distribution of marital status for the U.S. adult population.

alternative hypothesis:1. The data do not fit the distribution of marital status for the U.S. adult population.

b)

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

c) ₃\

d) test statistic =16.80

p value =0.0008

Explain what the p-value means for this problem. :

3. H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.

ii)Decision:  1. reject the null hypothesis

iii)Since alpha > p-value, we reject the null hypothesis

iv)

1. There is sufficient evidence to conclude that the data do not fit the distribution of marital status for the U.S. adult population.