A school social worker wants to determine if the grade distribution of home-scho

Question

A school social worker wants to determine if the grade distribution of home-schooled children is different in her district than nationally. A national statistical center provided her with the data in the first table below, which represent the relative frequency of home-schooled children by grade level. She obtains a sample of 25 home-schooled children within her district that yields the data in the second table below. Complete parts (a) and (b) below. (a) Because of the low cell counts, combine cells into three categories K-3, 4-8, and 9-12. (Type integers or decimals rounded to three decimal places as needed.)

Explanation / Answer

From the above table we use it and club classes to get a new table as:

Since first class is from k-3, so its frequency will be 7+9=16.

Second class is from 4-8,so its frequency will be 6+2=8.

Third classe's freqency is 1.

For finding relative frequency we divide each frequency by the total frequency.

For finding expected frequency we use the table given by national statistical center.

We make the relative frequencies of the given table as our classes in the new table like:

First class K-3 relative frequency is 0.049+0.294=0.343

Similarly for the other classes we find out.

Then we multiply each relative frequency by 25 to get the expected frequencies of each of the classes.

Grade Relative Frequency Observed Frequency Expected Frequency K-3             0.64               16             8.575 4-8             0.32                8              7.7 9-12             0.04                1             8.725

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