A recent national report states the marital status distribution of the male population age 18 or older is as follows: Never Married (32.3%), Married (55.3%), Widowed (2.4%), Divorced (10%).

Question

A recent national report states the marital status distribution of the male population age 18 or older is as follows: Never Married (32.3%), Married (55.3%), Widowed (2.4%), Divorced (10%). The table below shows the results of a random sample of 1620 adult men from California. Test the claim that the distribution from  California is as expected at the  = 0.10 significance level.

1. Complete the table by filling in the expected frequencies. Round to the nearest whole number:

Frequencies of Marital StatusOutcomeFrequencyExpected Frequency
Never Married	507
Married	909
Widowed	54
Divorced	150

1. What is the correct statistical test to use?
2. Select an answer Paired t-test Independence Homogeneity Goodness-of-Fit Correct 
3. What are the null and alternative hypotheses?
4.  
5. The distribution of marital status in California is not the same as it is nationally.
6. The distribution of marital status in California is the same as it is nationally.
7. Marital status and residency are independent.
8. Marital status and residency are dependent.
9. Cor
10. Marital status and residency are independent.
11. Marital status and residency are dependent.
12. The distribution of marital status in California is the same as it is nationally.
13. The distribution of marital status in California is not the same as it is nationally.
14. Correct
15. The degrees of freedom = Correct

1. The test-statistic for this data =  (Please show your answer to three decimal places.) 

1. The p-value for this sample = (Please show your answer to four decimal places.) 

1. The p-value is Select an answer greater than less than (or equal to) Correct   

1. Based on this, we should Select an answer fail to reject the null reject the null accept the null Correct 

1. Thus, the final conclusion is... 
2. There is sufficient evidence to conclude that the distribution of marital status in California is the same as it is nationally.
3. There is sufficient evidence to conclude that marital status and residency are dependent.
4. There is insufficient evidence to conclude that marital status and residency are dependent.
5. There is insufficient evidence to conclude that the distribution of marital status in California is not the same as it is nationally.
6. There is sufficient evidence to conclude that the distribution of marital status in California is not the same as it is nationally.

Answer 1

Hi Annie,

#1.

Expected count=np

n=total sample size

p=expected proportion

For example, the first category, never married:

n=1620

p=0.323--32.3% converted to decimal

EC= 523

Repeat the process for the rest of the categories.

#2 and 3

Think about what you are trying to find out. You want to know if the California data fits the national data well. Answer based on this.

#4-7

Null means nothing, as in no difference. Alternative means the opposite, as in some significant difference. So does the CA distribution differ from the US distribution? Choose a null and alternative hypothesis based on that question.

#8-1

df= k -1, where k is the number of categories. In this case, you have 4 categories--never married, married, widowed, divorced, so compute degrees of freedom based on that.

#8-2

X² = Sum (Observed Count - Expected Count)²/Expected Count. So, first one, never married:

Observed= 507

Expected= 523

X²-Component = (507-523)²/523 = 0.489

Compute X² components for the other three categories the same way, then add them together to get the X² test statistic.

#8-3

In Microsoft Excel, type:

=CHISQ.RT(X², df) where:

X²= test-statistic above

df=degrees of freedom above

This will yield a p-value.

#8-4

Reject the null if p<0.10. Fail to reject if p>0.10.

#8-5

That depends on your hypothesis decision. If you reject the null, you are saying there is sufficient evidence to conclude that California's marital status distribution differs from the national distribution. If you fail to reject, you are saying that there is not sufficient evidence to make that conclusion.

I hope this helps.