Question

The accuracy of a census report on a city in southern California was questioned by some...

The accuracy of a census report on a city in southern California was questioned by some government officials. A random sample of 1215 people living in the city was used to check the report, and the results are shown below.

Ethnic Origin Census Percent Sample Result
Black 10%         131        
Asian 3%         50        
Anglo 38%         469        
Latino/Latina 41%         495        
Native American 6%         57        
All others 2%         13        

Using a 1% level of significance, test the claim that the census distribution and the sample distribution agree.

(a) What is the level of significance?


State the null and alternate hypotheses.

H0: The distributions are different.
H1: The distributions are different.

H0: The distributions are the same.
H1: The distributions are the same.   

H0: The distributions are different.
H1: The distributions are the same.

H0: The distributions are the same.
H1: The distributions are different.


(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes

No    


What are the degrees of freedom?


(c) Estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100   

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005


(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.


(e) Interpret your conclusion in the context of the application.

At the 1% level of significance, the evidence is sufficient to conclude that census distribution and the ethnic origin distribution of city residents are different.

At the 1% level of significance, the evidence is insufficient to conclude that census distribution and the ethnic origin distribution of city residents are different.  

Homework Answers

Answer #1

The statistical software output for this problem is :

(a)

H0: The distributions are the same.
H1: The distributions are different.

(b)

Test statistics = 14.638

Yes

chi square

Degrees of freedom = 5

(c)

0.010 < P-value < 0.025

(d)

Since the P-value > α, we fail to reject the null hypothesis.

(e)

At the 1% level of significance, the evidence is insufficient to conclude that census distribution and the ethnic origin distribution of city residents are different.

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