Question

A recent national report states the marital status distribution of the male population age 18 or older is as follows:
Never Married (31.6%),
Married (54.6%),
Widowed (2.4%),
Divorced (11.4%).

The table below shows the results of a random sample of 1744 adult men from California. Test the claim that the distribution from  California is as expected at the αα = 0.10 significance level.

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

   Frequencies of Marital Status

   Outcome	Frequency	Expected Frequency
   Never Married	552
   Married	939
   Widowed	67
   Divorced	186

2. What are the null and alternative hypotheses?
   H0:H0: Select an answer Marital status and residency are dependent. Marital status and residency are independent. The distribution of marital status in California is the same as it is nationally. The distribution of marital status in California is not the same as it is nationally.
   
   
   Ha:Ha:
   • Marital status and residency are independent.
   • The distribution of marital status in California is the same as it is nationally.
   • Marital status and residency are dependent.
   • The distribution of marital status in California is not the same as it is nationally.
3. The degrees of freedom =
   
   
4. The test-statistic for this data =  (Please show your answer to two decimal places.)
   
   
5. 
   
6. Based on this, we should
   • reject the null
   • accept the null
   • fail to reject the null
   
   
   
7. Thus, the final conclusion is...
   • There is sufficient evidence to conclude that marital status and residency are dependent.
   • There is sufficient evidence to conclude that the distribution of marital status in California is not the same as it is nationally.
   • There is insufficient evidence to conclude that the distribution of marital status in California is not the same as it is nationally.
   • There is insufficient evidence to conclude that marital status and residency are dependent.
   • There is sufficient evidence to conclude that the distribution of marital status in California is the same as it is nationally.

Answer 1

1).the table be:-

Outcome	Frequency	Expected Frequency
Never Married	552	1744*0.316 = 551
Married	939	1744*0.546 = 952
Widowed	67	1744*0.024 = 42
Divorced	186	1744*0.114 = 199

2).hypothesis:-

H₀: The distribution of marital status in California is the same as it is nationally.

H_a: The distribution of marital status in California is not the same as it is nationally.

3). degrees of freedom = (4-1) = 3

4).the test statistic be:-

  

  

[ here, this value a bit smaller..as in question we have instructed to convert the expected frequency to nearest whole number....but if you use the actual values the value of test statistic will be 16.12 ]

5).the rejection region is :-

[ chi square critical value for df=3,alpha=0.10 is = 6.25 ]

6).Based on this, we should : Reject the null

[ as chi square = 15.91 > 6.25 ]

7).Thus, the final conclusion is:-

There is sufficient evidence to conclude that the distribution of marital status in California is not the same as it is nationally.

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