91Ó°ÊÓ

Use the following information to answer the next two exercises: The columns in Table contain the

Race/Ethnicity of U.S. Public Schools for a recent year, the percentages for the Advanced Placement Examinee Population for that class, and the Overall Student Population. Suppose the right column contains the result of a survey of 1,000 local students from that year who took an AP Exam.

Islander $10.20\%5.40\%113$Black or African-American $8.20\%14.50\%94$Hispanic or Latino $15.50\%15.90\%$136 American Indian or Alaska Native$0.60\%1.20\%10$White $59.40\%61.60\%604$Not reported/other $6.10\%$$1.40\%43$

Perform a goodness-of-fit test to determine whether the local results follow the distribution of U.S. AP examinee population, based on ethnicity.

Step by step solution

01

Given Information

Given information are in the table

Total frequency is 1000

02

Explanation

Degree of freedom df = n-1

${\mathrm{χ}}^2=\underset{k}{∑}\frac{(O-E{)}^2}{E}$

${\mathrm{H}}_0=$The local results follow the distribution of the U.S. AP examinee population

${\mathrm{H}}_{\mathrm{a}}=$The local results do not follow the distribution of the U.S. AP examinee population

df =6-1=5

${\mathrm{χ}}^2=13.43$

$\mathrm{Î\pm }=0.05$

$p=0.0199$

When, $\mathrm{Î\pm }=0.05$the null hypothesis is rejected since $p$equals $<\mathrm{a}$. As a result, the local results do not match the distribution of the AP examinee population across the United States.

When$\mathrm{Î\pm }=0.01$, the null hypothesis is not rejected. As a result, the data are insufficient to determine if the local results are representative of the US AP examinee population.

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