The accuracy of a census report on a city in southern Californiawas questioned by some government officials. A random sample of1215 people living in the city was used to check the report, andthe results are shown below.

EthnicOrigin	CensusPercent	SampleResult
Black	10%       Â	139       Â
Asian	3%       Â	35       Â
Anglo	38%       Â	469       Â
Latino/Latina	41%       Â	503       Â
Native American	6%       Â	56       Â
All others	2%       Â	13       Â

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

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are the same.
H₁: The distributions aredifferent.H₀: The distributions aredifferent.
H₁: The distributions aredifferent.    H₀: Thedistributions are the same.
H₁: The distributions are thesame.H₀: The distributions are different.
H₁: The distributions are the same.

(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?

YesNo    

What sampling distribution will you use?

uniformnormal    binomialchi-squareStudent'st

What are the degrees of freedom?


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

P-value > 0.1000.050 < P-value <0.100    0.025 < P-value <0.0500.010 < P-value < 0.0250.005 <P-value < 0.010P-value < 0.005

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

Since the P-value > α, we fail to rejectthe null hypothesis.Since the P-value > α, wereject the null hypothesis.    Since theP-value ≤ α, we reject the null hypothesis.Sincethe P-value ≤ α, we fail to reject the nullhypothesis.

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

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