A school social worker wants to determine if the grade distribution of home-schooled children is different in her district than nationally. The U.S. National Center for Education Statistics provided her with the following data, which represent the relative frequency of home-schooled children by grade level.

Grade                                             Relative Frequency
K .....................................................            0.076
1–3 .................................................            0.253
4–5 .................................................            0.158
6–8 .................................................            0.235
9–12 ...............................................            0.278

She obtains a sample of 25 home-schooled children within her district that yields the following data:
Grade                                              Frequency
K .................................................            6
1–3 .............................................            9
4–5 .............................................            3
6–8 .............................................            4
9–12 ...........................................            3

(a) Because of the low cell counts, combine cells into three categories K–3, 4–8, and 9–12.

(b) Is the grade distribution of home-schooled children different in her district from the national grade distribution at the a = 0.05 level of significance?