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S W A local politician is concerned that a program for the homeless in her city is discriminating against blacks and other minorities. The following data were taken from a random sample of black and white homeless people. Race Received Services? Black White Totals Yes 6 7 13 No Totals 4 10 9 16 13 26 a. Is there a statistically significant relationship between race and whether the person has received services from the program? b. Compute column percentages for the table to clarify the pattern of the relationship. Which group was more likely to get services?

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Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

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Chapter
Section
BuyFindarrow_forward

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 10, Problem 10.3P
Textbook Problem
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S W A local politician is concerned that a program for the homeless in her city is discriminating against blacks and other minorities. The following data were taken from a random sample of black and white homeless people.

Race
Received Services? Black White Totals
Yes 6 7 13
No
Totals
4 10 9 16 13 26

a. Is there a statistically significant relationship between race and whether the person has received services from the program?

b. Compute column percentages for the table to clarify the pattern of the relationship. Which group was more likely to get services?

To determine

(a)

To find:

The chi square value for the given information and test for its significance.

Explanation of Solution

Given:

The given statement is,

A local politician is concerned that a program for the homeless in her city is discriminating against blacks and other minorities.

The given table of information is,

Race
Received Services? Black White Totals
Yes 6 7 13
No 4 9 13
Totals 10 16 26

Approach:

The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.

The five step model for hypothesis testing is,

Step 1. Making assumptions and meeting test requirements.

Step 2. Stating the null hypothesis.

Step 3. Selecting the sampling distribution and establishing the critical region.

Step 4. Computing test statistics.

Step 5. Making a decision and interpreting the results of the test.

Formula used:

For a chi square, the expected frequency fe is given as,

fe=Rowmarginal×ColumnmarginalN

Where N is the total of frequencies.

The chi square statistic is given by,

χ2(obtained)=(fofe)2fe

Where fo is the observed frequency,

And fe is the expected frequency.

The degrees of freedom for the bivariate table is given as,

df=(r1)(c1)

Where r is the number of rows and c is the number of columns.

Calculation:

From the given information,

The observed frequency is given as,

fe=Rowmarginal×ColumnmarginalN....(1)

Substitute 13 for row marginal, 10 for column marginal and 26 for N in equation (1).

f1=10×1326=5

Substitute 13 for row marginal, 16 for column marginal and 26 for N in equation (1).

f2=13×1626=8

Substitute 13 for row marginal, 10 for column marginal and 26 for N in equation (1).

f3=13×1026=5

Substitute 13 for row marginal, 16 for column marginal and 26 for N in equation (1).

f4=13×1626=8

Consider the following table,

6.25 fo fe fofe (fofe)2 (fofe)2/fe
6 5 1 1 0
To determine

(b)

To find:

The chi square value for the given information and test for its significance.

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