4. The median test for independent samples Aa Aa E A teacher wants to see which

Question

4. The median test for independent samples Aa Aa E A teacher wants to see which activity best improves second grade students' arithmetic scores. She randomly selects 30 second grade students and randomly splits them into three groups, each of which will perform a different activity for 15 minutes. One group plays math games that involve arithmetic. Another group uses flash cards to memorize math facts. The last group reads a book about dinosaurs. At the end of the 15-minute activity, she has each student take an arithmetic test with 30 addition and subtraction problems. The table below contains the scores for the 30 students. Silent Reading Math Games Flash Cards 30 27 24 26 17 18 15 23 27 27 15 12 24 29 14 23 21 28 25 27 19 18 17 28 18 22 29 The teacher wants to find out if there is a significant relationship between which 15-minute activity the children do and their scores on the subsequent arithmetic test. She uses a median test to evaluate whether these three groups share a common median score. The overall median for the 30 students is 23.5. using the information in the table above, fill out the table below with the observed frequencies of the number of students above and below the median in each the three groups. of

Explanation / Answer

From following results we have the filled in tables

The chi-sqaure test statistic is 7.20 with df=5 and alpha=0.05, the teacher decided to reejct the null hypothesis and conclude that the median scores of these three groups are different

Chi-Square Test Observed Frequencies Activity Calculations Score Silent Reading Math Games Flash Cards Total fo-fe Above Median 5 8 2 15 0 3 -3 Below Median 5 2 8 15 0 -3 3 Total 10 10 10 30 Expected Frequencies Activity Score Silent Reading Math Games Flash Cards Total (fo-fe)^2/fe Above Median 5 5 5 15 0 1.8 1.8 Below Median 5 5 5 15 0 1.8 1.8 Total 10 10 10 30 Data Level of Significance 0.05 Number of Rows 2 Number of Columns 3 Degrees of Freedom 2 Results Critical Value 5.991464547 Chi-Square Test Statistic 7.2 p-Value 0.027323722 Reject the null hypothesis Expected frequency assumption        is met.

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