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 Black Census Sample Result Percent 10% 123 Asian 3% 36 Anglo 38% 471 Latino/Latina 41% 512 Native American 6% 60 All others 2% 13 I 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. OH: The distributions are the same. H₁: The distributions are different. OH: The distributions are different. H: The distributions are the same. OH: The distributions are different. H₁: The distributions are different. OH: The distributions are the same. 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? O Student's t O normal O uniform O binomial O chi-square What are the degrees of freedom? (c) Estimate the P-value of the sample test statistic. OP-value>0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value < 0.050 O 0.010 < P-value < 0.025 0.005 < P-value < 0.010 OP-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>, we reject the null hypothesis. O Since the P-value sa, we reject the null hypothesis. O Since the P-values, 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 condude 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.
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 Black Census Sample Result Percent 10% 123 Asian 3% 36 Anglo 38% 471 Latino/Latina 41% 512 Native American 6% 60 All others 2% 13 I 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. OH: The distributions are the same. H₁: The distributions are different. OH: The distributions are different. H: The distributions are the same. OH: The distributions are different. H₁: The distributions are different. OH: The distributions are the same. 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? O Student's t O normal O uniform O binomial O chi-square What are the degrees of freedom? (c) Estimate the P-value of the sample test statistic. OP-value>0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value < 0.050 O 0.010 < P-value < 0.025 0.005 < P-value < 0.010 OP-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>, we reject the null hypothesis. O Since the P-value sa, we reject the null hypothesis. O Since the P-values, 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 condude 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.
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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Question
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.
Ethnic Origin
Black
Census
Sample
Result
Percent
10%
123
Asian
3%
36
Anglo
38%
471
Latino/Latina
41%
512
Native American
6%
60
All others
2%
13
I 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.
OH: The distributions are the same.
H₁: The distributions are different.
OH: The distributions are different.
H: The distributions are the same.
OH: The distributions are different.
H₁: The distributions are different.
OH: The distributions are the same.
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?
O Student's t
O normal
O uniform
O binomial
O chi-square
What are the degrees of freedom?
(c) Estimate the P-value of the sample test statistic.
OP-value>0.100
O 0.050 < P-value < 0.100
O 0.025 < P-value < 0.050
O 0.010 < P-value < 0.025
0.005 < P-value < 0.010
OP-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>, we reject the null hypothesis.
O Since the P-value sa, we reject the null hypothesis.
O Since the P-values, 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 condude 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.
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