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.
Ethnic Origin | Census Percent | Sample Result |
Black | 10% | 121 |
Asian | 3% | 47 |
Anglo | 38% | 486 |
Latino/Latina | 41% | 486 |
Native American | 6% | 62 |
All others | 2% | 13 |
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 different.
H1: The distributions are different.
H0: The distributions are the same.
H1: The distributions aredifferent.
H0: The distributions are the same.
H1: The distributions are the same.
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?
Yes
No
What sampling distribution will you use?
uniform
chi-square
Student's t
normal
binomial
What are the degrees of freedom?
(c) Estimate the P-value of the sample teststatistic.
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 rejector fail to reject the null hypothesis that the population fits thespecified distribution of categories?
Since the P-value > ?, we fail to rejectthe null hypothesis.
Since the P-value > ?, we reject the nullhypothesis.
Since the P-value ? ?, we reject the nullhypothesis.
Since the P-value ? ?, we fail to reject thenull hypothesis.
(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 of significance, the evidence is insufficient toconclude that census distribution and the ethnic origindistribution of city residents are different.
