The following table shows the proportion of home schooled children by grade leve

Question

The following table shows the proportion of home schooled children by grade level irn U.S. Grade level Proportion in U.S.0.076 4-5 9 -12 0.253 0.158 0.235 0.278 A social worker wants to determine if the grade level distribution of home-schooled children is different in her district than nationally. She obtains a sample of 50 home- schooled children within her district which yields the following data. Grade level 4-5 9 -12 12 18 Frequency in her district Conduct Chi-square goodness-of-fit test to test whether the grade level distribution of home-schooled children is different in her district than nationally at 0.05 level of significance

Explanation / Answer

chi-square = 26.1011

df = 4

p-value = 0.00003

As p-value is less than the significance level of 0.05, we reject null hypothesis

This means distribution is not in line with country level proportions.

Grade Level p Observed Frequency (Oi) Expected Frequency(Ei) (Oi - Ei)^2/Ei K 0.076 12 3.8 17.69473684 1-3 0.253 18 12.65 2.262648221 4-5 0.158 6 7.9 0.456962025 6-8 0.235 8 11.75 1.196808511 9-12 0.278 6 13.9 4.489928058 50 26.10108366

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