DETAILSMY NOTESASK YOUR TEACHER A city in a particular county has a population of 460,935; the population of the county is 9,519,338. Conduct a goodness of fit test at the 5% level to determine if the racial demographics of the city fit that of the county. Round expected frequency to two decimal places.RacePercent, countyExpected #, cityActual #, cityAmerican Indian and Alaska Native0.83687.483,969Asian11.9=55,416Black or African American9.8=68,614Native Hawaiian and other Pacific Islander0.3=5,592White, including Hispanic/Latino48.7=207,804Other23.5=95,164Two or more races5.0=24,376Part (a)State the null hypothesis.The data do not fit the distribution of the population of each race in the county.The data fit the distribution of the population of each race in the county. Part (b)State the alternative hypothesis.The data do not fit the distribution of the population of each race in the county.The data fit the distribution of the population of each race in the county. Part (c)What are the degrees of freedom?Part (d)State the distribution to use for the test.t7 t6Part (e)What is the test statistic? (Round your answer to the nearest whole number.)Part (f)What is the p-value? (Round your answer to four decimal places.)Explain what the p-value means for this problem.If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.Part (g)Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value. (Upload your file below.)This answer has not been graded yet.Part (h)Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write the appropriate conclusion.(i) Alpha:? = (ii) Decision:reject the null hypothesisdo not reject the null hypothesis (iii) Reason for decision:Since ? > p-value, we reject the null hypothesis.Since ? < p-value, we do not reject the null hypothesis. Since ? > p-value, we do not reject the null hypothesis.Since ? < p-value, we reject the null hypothesis.(iv) Conclusion:There is sufficient evidence to warrant a rejection of the claim that the data fit the distribution of the population of each race in the county.There is not sufficient evidence to warrant a rejection of the claim that the data fit the distribution of the population of each race in the county.

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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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DETAILS

MY NOTES

ASK YOUR TEACHER

A city in a particular county has a population of 460,935; the population of the county is 9,519,338. Conduct a goodness of fit test at the 5% level to determine if the racial demographics of the city fit that of the county. Round expected frequency to two decimal places.

Race	Percent, county	Expected #, city	Actual #, city
American Indian and Alaska Native	0.8	3687.48	3,969
Asian	11.9	=	55,416
Black or African American	9.8	=	68,614
Native Hawaiian and other Pacific Islander	0.3	=	5,592
White, including Hispanic/Latino	48.7	=	207,804
Other	23.5	=	95,164
Two or more races	5.0	=	24,376

Part (a)

State the null hypothesis.
The data do not fit the distribution of the population of each race in the county.

The data fit the distribution of the population of each race in the county.
Part (b)

State the alternative hypothesis.
The data do not fit the distribution of the population of each race in the county.

The data fit the distribution of the population of each race in the county.
Part (c)

What are the degrees of freedom?
Part (d)

State the distribution to use for the test.

t₇

t₆
Part (e)

What is the test statistic? (Round your answer to the nearest whole number.)
Part (f)

What is the p-value? (Round your answer to four decimal places.)

Explain what the p-value means for this problem.
If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.If H₀ is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value.

If H₀ is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value.
Part (g)

Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value. (Upload your file below.)

This answer has not been graded yet.
Part (h)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write the appropriate conclusion.
(i) Alpha:
? =

(ii) Decision:
reject the null hypothesis

do not reject the null hypothesis

(iii) Reason for decision:
Since ? > p-value, we reject the null hypothesis.

Since ? < p-value, we do not reject the null hypothesis.

  Since ? > p-value, we do not reject the null hypothesis.

Since ? < p-value, we reject the null hypothesis.

(iv) Conclusion:
There is sufficient evidence to warrant a rejection of the claim that the data fit the distribution of the population of each race in the county.

There is not sufficient evidence to warrant a rejection of the claim that the data fit the distribution of the population of each race in the county.

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