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. Census Sample Result Ethnic Origin Percent Black 10% 123 Asian 3% 46 471 Anglo Latino/Latina 38% 41% 505 Native American 6% 61 All others 2% 9. A USE SALT 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. O Ho: The distributions are the same. H,: The distributions are different. Ho: The distributions are different. H: The distributions are the same. O Ho: The distributions are the same. H,: The distributions are the same. O Ho: The distributions are different. H: 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? O Yes O No What sampling distribution will you use? O Student's t O normal O binomial O uniform O chi-square What are the degrees of freedom? (c) Estimate the P-value of the sample test statistic. O P-value > 0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value < 0.050 O 0.010 < P-value < 0.025 O 0.005 < P-value < 0.010 O 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? O Since the P-value > a, we fail to reject the null hypothesis. Since the P-value > a, we reject the null hypothesis. Since the P-value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O 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. O 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.
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. Census Sample Result Ethnic Origin Percent Black 10% 123 Asian 3% 46 471 Anglo Latino/Latina 38% 41% 505 Native American 6% 61 All others 2% 9. A USE SALT 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. O Ho: The distributions are the same. H,: The distributions are different. Ho: The distributions are different. H: The distributions are the same. O Ho: The distributions are the same. H,: The distributions are the same. O Ho: The distributions are different. H: 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? O Yes O No What sampling distribution will you use? O Student's t O normal O binomial O uniform O chi-square What are the degrees of freedom? (c) Estimate the P-value of the sample test statistic. O P-value > 0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value < 0.050 O 0.010 < P-value < 0.025 O 0.005 < P-value < 0.010 O 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? O Since the P-value > a, we fail to reject the null hypothesis. Since the P-value > a, we reject the null hypothesis. Since the P-value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O 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. O 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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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.
Census
Sample
Result
Ethnic Origin
Percent
Black
10%
123
Asian
3%
46
38%
Anglo
Latino/Latina
471
41%
505
Native American
6%
61
All others
2%
9.
A USE SALT
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.
O H: The distributions are the same.
H: The distributions are different.
O
Ho: The distributions are different.
H,: The distributions are the same.
O Ho: The distributions are the same.
H,: The distributions are the same.
O Ho: The distributions are different.
H: 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?
O Yes
O No
What sampling distribution will you use?
Student's t
O normal
O binomial
O uniform
O chi-square
What are the degrees of freedom?
(c) Estimate the P-value of the sample test statistic.
O P-value > 0.100
O 0.050 < P-value < 0.100
O 0.025 < P-value < 0.050
O 0.010 < P-value < 0.025
O 0.005 < P-value < 0.010
O 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?
O Since the P-value > a, we fail to reject the null hypothesis.
O
Since the P-value > a, we reject the null hypothesis.
Since the P-value s a, we reject the null hypothesis.
O Since the P-value s a, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
O 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.
O 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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