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S O C The state Department of Education has rated a sample of local school systems for compliance with state-mandated guidelines for quality. a. Is there a statistically significant relationship between the quality of a school system and the affluence of the community as measured by per capita income? b. Compute column percentages. Are high- or low- income communities more likely to have high-quality schools? Quality Per Capita income Low High Totals Low 16 8 24 High Totals 9 25 17 25 26 50

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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 10.7P
Textbook Problem
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S O C The state Department of Education has rated a sample of local school systems for compliance with state-mandated guidelines for quality.

a. Is there a statistically significant relationship between the quality of a school system and the affluence of the community as measured by per capita income?

b. Compute column percentages. Are high- or low- income communities more likely to have high-quality schools?

Quality Per Capita income
Low High Totals
Low 16 8 24
High
Totals
9 25 17 25 26 50

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,

The state Department of Education has rated a sample of local school systems for compliance with state-mandated guidelines for quality.

The given table of information is,

Quality Per Capita income
Low High Totals
Low 16 8 24
High 9 17 26
Totals 25 25 50

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 24 for row marginal, 25 for column marginal and 50 for N in equation (1).

f1=24×2550=12

Substitute 24 for row marginal, 25 for column marginal and 50 for N in equation (1).

f2=24×2550=12

Substitute 26 for row marginal, 25 for column marginal and 50 for N in equation (1).

f3=26×2550=13

Substitute 26 for row marginal, 25 for column marginal and 50 for N in equation (1).

f4=26×2550=13

Consider the following table,

6.25 fo fe fofe (fofe)2 (fofe)2/fe
16 12 4 16 1
To determine

(b)

To explain:

The given statement.

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