Question

In: Math

Census data for a city indicate that 29.0​% of the​ under-18 population is​ white, 26.2​% ​black,...

Census data for a city indicate that 29.0​% of the​ under-18 population is​ white, 26.2​% ​black, 33.2​% Latino, 9.5​% ​Asian, and 2.1​% other ethnicities. The city points out that of 25,577 police​ officers, 64.8​% are​ white,14.5​% ​black, 19.1​% ​Latino, 1.4​% ​Asian, and the remaining are other ethnicities. Do the police officers reflect the ethnic composition of the​ city's youth? Complete parts a through e below.

A) What is the appropriate test?

B) What is the null and alternative hypothesis?

C) What is the chi squared test statistic

D) what is the p value

Solutions

Expert Solution

Here we are provided with the census data for a city indicating the percentages of different communities of youths aswell as the respective proportions of police officers of the same communities.The total no. of police officers are also provided, 25577. We are to test wheather the police officers reflect the ethnic composition of the​ city's youth or not?

a. Here the appropriate test is the pearsonian test fror.

b. Thus the hypothesis is stated as: Ho:p1=p1*,p2=p2*,......,pk=pk* vs H1: at least on inequality in Ho

where pi s are the poppulation proportion of the ith class of the youth(unknown to us) and pi* s are the known value of the proportions(already given). and k is the total no. of class, here k=5

Now we take a random sample of size n(=25577) from the police poppulation and let fi is the sample members belonging to the ith class.

Thus the appropriate test statistics is given as:

T=  

Which under Ho follows a chi-sq distribution with (5-1) degrees of freedom and we reject our null hypothesis if the observed T is more than the upper alpha(=0.05) point of a chisq distribution with df=4

The observed T is given as: 26738.78; df=4

The upper alpha(=0.05) point of a chisq distribution with df=4 is 9.49

Thus we reject the null hypothesis and conclude based on our data that the police officers do not reflect the ethnic composition of the​ city's youth.

d. The p-value is given as: 2*min{P(T>Tobs),P(TTobs)) and it is given as 0 under Ho, in this case.

milcah answered 11 months ago
Next > < Previous

Related Solutions

Census data for a city indicate that 24.3% of the under-18 population is white, 28.9% black,...
Census data for a city indicate that 24.3% of the under-18 population is white, 28.9% black, 34.9% Latino, 9.3% Asian, and 2.6% other ethnicities. The city points out that of 25,667 police officers, 64.8% are white, 14.5% black, 19.1% Latino, 1.4% Asian, and the remaining are other ethnicities. Do the police officers reflect the ethnic composition of the city's youth? complete parts below. A) Test an appropriate hypothesis and state your results. Assume alpha α equals=0.05. What is the test​...
Census data for a city indicate that 64.4​% of the​ under-18 population is​ white, 14.5​% black,...
Census data for a city indicate that 64.4​% of the​ under-18 population is​ white, 14.5​% black, 19.5​% Latino, 1.4% ​Asian, and 0.2​% other ethnicities. The city points out that of 25,0092 police​ officers, 64.8​% are​ white, 14.5​% ​black, 19.1​% ​Latino, and 1.4​% Asian. Do the police officers reflect the ethnic composition of the​ city's youth? Test an appropriate hypothesis and state your conclusion.​ (Assume a significance level of alphaαequals=0.05​) A) Compute the chi-square statistic B) Compute the P-Value
White White Black Black Other Other Years Cases Population Cases Population Cases Population < 50 3,371...
White White Black Black Other Other Years Cases Population Cases Population Cases Population < 50 3,371 6,911,876 1,466 3,297,033 791 1,823,497 50-54 2,007 834,541 715 311,774 364 177,808 55-59 2,026 757,364 768 272,111 331 160,126 60-64 2,483 661,428 776 223,112 362 137,703 65-69 2,191 485,851 618 143,872 283 89,912 70+ 5,341 1,185,358 1,234 288,056 548 206,271 8. Calculate the age-specific rates for each racial group. Graph the age-specific rates for each racial group. *Please use the graph to answer the...
Black Hispanic White Pass 9 6 41 Fail 18 17 27 Use this data and a...
Black Hispanic White Pass 9 6 41 Fail 18 17 27 Use this data and a 0.05 significance level to test the claim that less than 58% of the minority candidates (Black and Hispanic candidates grouped together) pass the lieutenants exam. Sample proportion, p-hat = A. 0.26 B. 0.17 C. 0.31 D. 0.62 Test Statistic, z = A. -3.27 B. -2.71 C. 1.12 D. 0.82 Critical z = A. -1.645 B. 1.645 C. -1.645, 1.645 D. -1.96, 1.96 P-Value =...
According to the U.S. Census Bureau, 69% of children under the age of 18 years in...
According to the U.S. Census Bureau, 69% of children under the age of 18 years in the United States lived with two parents in 2009. Suppose that in a recent sample of 2000 children, 1267 were living with two parents. a. Using the critical value approach and test whether the current percentage of all children under the age of 18 years in the United States who live with two parents is different from 69%. Round your answer for z to...
According to the Census Bureau, the distribution by ethnic background of the New York City population...
According to the Census Bureau, the distribution by ethnic background of the New York City population in a recent year was Hispanic: 28% Black: 24% White: 35% Asian: 12% Others: 1% The manager of a large housing complex in the city wonders whether the distribution byrace of the complex’s residents is consistent with the population distribution. To find out,she records data from random sample of 800 residents. The table below displays the sample data. Race Hispanic Black White Asian Others...
In a city, the racial make up is 68% White, 24% Black, 5% Asian and the...
In a city, the racial make up is 68% White, 24% Black, 5% Asian and the remainder are classified as Other. A report on traffic stops by police officers in this city is being used to determine if the racial makeup of the motorists stopped reflect the racial makeup of the city. The race of drivers stopped by police officers over a 4 month period is recorded in the table. Determine if there is sufficient evidence to warrant the claim...
In a city, the racial make up is 68% White, 24% Black, 5% Asian and the...
In a city, the racial make up is 68% White, 24% Black, 5% Asian and the remainder are classified as Other. A report on traffic stops by police officers in this city is being used to determine if the racial makeup of the motorists stopped reflect the racial makeup of the city. The race of drivers stopped by police officers over a 4 month period is recorded in the table. Determine if there is sufficient evidence to warrant the claim...
Topic: Comparing support for including ethnic consideration in college admissions between White and Black Populations. Data:...
Topic: Comparing support for including ethnic consideration in college admissions between White and Black Populations. Data: Whites (659 of 2,997 say Yes, race should be a factor) Blacks (577 of 1,518 say Yes, race should be a factor) Provide the following: 1. Summary Statistics 2. T-Test (or Confidence Interval) 3. Hypothesis Test 4. Regression
Data for an economy. Population:    22.5 million Population under the age of 16 years: 7.5 million...
Data for an economy. Population:    22.5 million Population under the age of 16 years: 7.5 million Discouraged workers: 250,000. Retired people: 1 million Structurally unemployed people: 220,000 Frictionally unemployed people: 220,000 Cyclically unemployed people: 2.2 million                                Using only these statistics above, answer the following four parts. Show full calculations. i. What is the labour force participation rate in economy X? ii. What is the current total unemployment rate in economy X? iii. What is the percentage of the adult...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT