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 Â Â Â Â Â Â Â | 121Â Â Â Â Â Â Â Â |
| Asian | 3%Â Â Â Â Â Â Â Â | 47Â Â Â Â Â Â Â Â |
| Anglo | 38%Â Â Â Â Â Â Â Â | 471Â Â Â Â Â Â Â Â |
| Latino/Latina | 41%Â Â Â Â Â Â Â Â | 504Â Â Â Â Â Â Â Â |
| Native American | 6%Â Â Â Â Â Â Â Â | 59Â Â Â Â Â Â Â Â |
| All others | 2%Â Â Â Â Â Â Â Â | 13Â Â Â Â Â Â Â 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 are thesame.H0: The distributions are different.
H1: The distributions aredifferent.    H0: Thedistributions are the same.
H1: The distributions aredifferent.H0: The distributions aredifferent.
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   Â
What sampling distribution will you use?
Student'stnormal    uniformbinomialchi-square
What are the degrees of freedom?
(c) Estimate the P-value of the sample test statistic.
P-value > 0.1000.050 < P-value <0.100Â Â Â Â 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.
